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RETIREMENT STRATEGY 1

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This activity will examine one retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete a PAM table. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 1: SAVINGS EARLY PLAN

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 1 of the Comparison Table in Part 3 of the Project.

STRATEGY 1: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2042, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 23 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 23 years, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 2 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 1

TOTAL POINTS 28

STRATEGY 1: SAVING EARLY PLAN (14 POINTS)

Question 1 Work (8 points)

5 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified

2 points – Correct substitution of values and correct answer

Question 2 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 3 Work (2 points)

1 point – Correct calculation of interest earned

Submission of picture of work in a single document (2 points)

1 point – Picture in focus & showing all work for question 1 in single pdf document for project

1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

STRATEGY 1: SAVING LATER PLAN (14 POINTS)

Question 1 Work (8 points)
5 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 3 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

RETIREMENT STRATEGY 2

This activity will examine a second retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete PAM tables. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 2: SAVINGS EARLY PLAN

Assume that you are 22 years old and are started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2022. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?

After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 3 of the Comparison Table in Part 3 of the Project.

STRATEGY 2: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2042. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?
After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 4 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 2

TOTAL POINTS 42

STRATEGY 2: SAVING EARLY PLAN (21 POINTS)

Question 1 Work (7 points)

4 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 2 Work (1 point)

1 point – Correct calculation of years left

Question 3 Work (7 points)

4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 4 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 5 Work (2 points)

1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)

1 point – Picture(s) in focus & showing all work for questions 1 and 2 in single pdf document for project

1 point – Picture(s) in focus & showing all work for questions 3, 4, and 5 in single pdf document for project

STRATEGY 2: SAVING LATER PLAN (21 POINTS)

Question 1 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (1 point)
1 point – Correct calculation of years left
Question 3 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 4 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 5 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

COMPARISON TABLE OF RETIREMENT SAVINGS PLANS

In previous activities, the amounts available at retirement, amounts paid into the retirement account, and the amount of interest earned have been computed for one or more retirement saving strategies with assumptions for starting to save when in your twenties (Saving Early plan) or for starting to save when in your forties (Saving Later plan). This activity is designed to help organize the results so the results may be analyzed, and some conclusions can be made.

DIRECTIONS

Create a Comparison Table with the results of the different Retirement Saving Plan strategies studied earlier in this project. See Retirement Strategy 1 and 2. The Comparison Table created below along with a picture of all handwritten computations needed to complete the table should be included in the Investment Project results document. See Overall Presentation and Submission.

CREATE A COMPARISON TABLE

Create a table comparing the amounts available at retirement, amount paid into the retirement account, and the amount of interest earned under the Saving Early plan and the Saving Later plan for each investment strategy. Include a brief description of the investment strategy in your table. Add footnotes to your table that clarify what is meant by a positive versus a negative number.

The Comparison Table must be created initially in a word processing program and be typed. Students will not receive credit for handwritten tables.

The first four rows of the table summarize the results from Retirement Strategy 1 and from Retirement Strategy 2.

The next four rows summarize the differences in these amounts as indicated below:

Compute and include in the table, the following columns of differences:

the difference in the amount available at retirement

the difference in the amount paid into the retirement account

the difference in the amount of interest earned

between each of the following:

the Saving Early and Saving Later plans for each investment strategy (one row for Retirement Strategy 1 and a separate row for Retirement Strategy 2)

each pair of Saving Early plans

each pair of Saving Later plans

An example of a blank Comparison Table of Retirement Savings Plans might look like the following:

Investment Project Sample Comparison Table

Total Possible Points 13

No Credit earned if Comparison Table is handwritten. Must be typed to earn credit.

Row 1 of Table (0.75 points)

0.25 point for each correct number in row

Row 2 of Table (0.75 points)

0.25 point for each correct number in row

Row 3 of Table (0.75 points)

0.25 point for each correct number in row

Row 4 of Table (0.75 points)

0.25 point for each correct number in row

Row 5 of Table (2.25 points)

0.25 point for each correct subtraction

0.5 point for each correct amount in the row

Row 6 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 7 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 8 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Included Table in single Project Results pdf document (1 points)

1 point – Included Comparison Table and picture(s) in focus & showing all subtractions in single pdf document for project

ANALYSIS OF RETIREMENT SAVINGS

In previous activities, key amounts related to different Retirement Strategies have been computed. The amounts were computed using assumptions that the saving started early in your twenties and using assumptions that the saving occurred later and started in your forties. In the last activity, differences in the amounts from the different Retirement Strategies were computed, and all amounts were summarized in a Comparison Table. This activity is designed to use the Comparison Table and allow you to reflect on what you have learned and to analyze the different strategies so that some conclusions about good strategies for when and how to save for retirement can be made.

DIRECTIONS

Write a short paragraph (at least 8 sentences) explaining what lessons you have learned about saving for retirement from the activities in the Investment Project and analyzing the results as indicated below. Your paragraph should be typed and grammatically correct. Include your typed paragraph in the Investment Project results document. See Overall Presentation and Submission.

ANALYSIS PARAGRAPH CONTENT REQUIREMENTS

Your paragraph should include the following:

Identify at least two specific things you have learned.

Explain when you should start saving for retirement and why

Explain what you think is the best strategy for saving for retirement is. Be specific. Include a savings plan and how much you expect to have at retirement.

Explain why there is a difference in the amount available at retirement if you start saving later.

Explain whether or not older individuals should start saving for retirement and why you think this. What specific strategy, if any, should they use. Include a savings plan and how much they would have at retirement.

Total Possible Points 10

No Credit earned if Analysis Paragraph is handwritten. Must be typed to earn credit.

Overall (2 points)

2 points for well written, coherent paragraph with at least 8 sentences

Lessons Learned (2 points)

1 point for each explained lesson learned

When to Save (1point)

1 point for reasonable explanation of when should start saving for retirement and why. No credit without an explanation of why.

Retirement Saving Strategy (2 points)

0.5 points for proposing a reasonable strategy for saving for retirement

1.5 points for including amount to be saved and correct amount expected at retirement

Difference in Retirement Amounts (1 point)

1 point for correctly explaining why there is a difference in the amount available at retirement if you start saving later

Saving Strategy when Older (2 points)

1 point for a reasonable explanation of whether older individuals should start saving for retirement and why

1 point for a reasonable strategy for saving including amount to be saved and correct amount expected at retirement

Investment Project

NAME

Retirement Savings Strategy 1

Strategy 1: Savings Early Plan

Strategy 1: Savings Later Plan

Retirement Savings Strategy 2

Strategy 2: Savings Early Plan

Strategy 2: Savings Later Plan

3 Comparison Table of Retirement Savings Plans
(### will be actual numbers in your document)

Amount

Available at
Retirement

Amount Paid
into Retirement

Account

Amount of
Interest Earned

Strategy 1: Saving Early Plan
Invest \$250 each month starting

at age 22 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 1: Saving Later Plan
Invest \$250 each month starting

at age 42 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 22 for 15 years
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 42 for 15 years
#,###,###.## ###,###.## #,###,###.##

Differences in Strategy 1 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Strategy 2 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Saving Early Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

Differences in Saving Later Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

1A positive number means that the amount from the Saving Early plan was higher than the amount from the
Saving Later plan while a negative number means the amount from the Saving Later plan was higher.

2 A positive number means that the amount from Investment Strategy 1 was higher than the amount from
Investment Strategy 2 while a negative number means the amount from Investment Strategy 2 was higher.

4 Analysis of Retirement Savings

Insert typewritten paragraph answering all questions from this part of the project.

MATH-132Unit 2

Exam Sheet

I Prt= P = principal

1
ntr

A P
n

 
= + 

 

1

nt

A
P

r
n

=
 + 
 

I = simple interest

r = annual interest rate

rtA Pe= rt
A

P
e

= t = time or term of investment
or loan (in years)

1 1
ntr

M
n

A
r
n

   + −    =
 
 
 

1 1

nt

r
A

nM
r
n

 
 
 =

   + −    

A = future value or amount
accumulated

n = number of times interest is
compounded per year

1 1
ntr
M
n

P
r
n

−   − +    =
 
 
 

1 1
nt

r
P

nM
r
n

 
 
 =

   − +    

e = Euler’s number

M = installment payment or
monthly payment

1 1
nr

Y
n

 
= + − 
 

Y = effective annual interest
rate or effective annual yield

RETIREMENT STRATEGY 1

This activity will examine one retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete a PAM table. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 1: SAVINGS EARLY PLAN

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 1 of the Comparison Table in Part 3 of the Project.

STRATEGY 1: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2042, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 23 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 23 years, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 2 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 1

TOTAL POINTS 28

STRATEGY 1: SAVING EARLY PLAN (14 POINTS)

Question 1 Work (8 points)

5 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified

2 points – Correct substitution of values and correct answer

Question 2 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 3 Work (2 points)

1 point – Correct calculation of interest earned

Submission of picture of work in a single document (2 points)

1 point – Picture in focus & showing all work for question 1 in single pdf document for project

1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

STRATEGY 1: SAVING LATER PLAN (14 POINTS)

Question 1 Work (8 points)
5 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 3 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

RETIREMENT STRATEGY 2

This activity will examine a second retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete PAM tables. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 2: SAVINGS EARLY PLAN

Assume that you are 22 years old and are started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2022. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?

After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 3 of the Comparison Table in Part 3 of the Project.

STRATEGY 2: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2042. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?
After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 4 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 2

TOTAL POINTS 42

STRATEGY 2: SAVING EARLY PLAN (21 POINTS)

Question 1 Work (7 points)

4 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 2 Work (1 point)

1 point – Correct calculation of years left

Question 3 Work (7 points)

4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 4 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 5 Work (2 points)

1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)

1 point – Picture(s) in focus & showing all work for questions 1 and 2 in single pdf document for project

1 point – Picture(s) in focus & showing all work for questions 3, 4, and 5 in single pdf document for project

STRATEGY 2: SAVING LATER PLAN (21 POINTS)

Question 1 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (1 point)
1 point – Correct calculation of years left
Question 3 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 4 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 5 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

COMPARISON TABLE OF RETIREMENT SAVINGS PLANS

In previous activities, the amounts available at retirement, amounts paid into the retirement account, and the amount of interest earned have been computed for one or more retirement saving strategies with assumptions for starting to save when in your twenties (Saving Early plan) or for starting to save when in your forties (Saving Later plan). This activity is designed to help organize the results so the results may be analyzed, and some conclusions can be made.

DIRECTIONS

Create a Comparison Table with the results of the different Retirement Saving Plan strategies studied earlier in this project. See Retirement Strategy 1 and 2. The Comparison Table created below along with a picture of all handwritten computations needed to complete the table should be included in the Investment Project results document. See Overall Presentation and Submission.

CREATE A COMPARISON TABLE

Create a table comparing the amounts available at retirement, amount paid into the retirement account, and the amount of interest earned under the Saving Early plan and the Saving Later plan for each investment strategy. Include a brief description of the investment strategy in your table. Add footnotes to your table that clarify what is meant by a positive versus a negative number.

The Comparison Table must be created initially in a word processing program and be typed. Students will not receive credit for handwritten tables.

The first four rows of the table summarize the results from Retirement Strategy 1 and from Retirement Strategy 2.

The next four rows summarize the differences in these amounts as indicated below:

Compute and include in the table, the following columns of differences:

the difference in the amount available at retirement

the difference in the amount paid into the retirement account

the difference in the amount of interest earned

between each of the following:

the Saving Early and Saving Later plans for each investment strategy (one row for Retirement Strategy 1 and a separate row for Retirement Strategy 2)

each pair of Saving Early plans

each pair of Saving Later plans

An example of a blank Comparison Table of Retirement Savings Plans might look like the following:

Investment Project Sample Comparison Table

Total Possible Points 13

No Credit earned if Comparison Table is handwritten. Must be typed to earn credit.

Row 1 of Table (0.75 points)

0.25 point for each correct number in row

Row 2 of Table (0.75 points)

0.25 point for each correct number in row

Row 3 of Table (0.75 points)

0.25 point for each correct number in row

Row 4 of Table (0.75 points)

0.25 point for each correct number in row

Row 5 of Table (2.25 points)

0.25 point for each correct subtraction

0.5 point for each correct amount in the row

Row 6 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 7 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 8 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Included Table in single Project Results pdf document (1 points)

1 point – Included Comparison Table and picture(s) in focus & showing all subtractions in single pdf document for project

ANALYSIS OF RETIREMENT SAVINGS

In previous activities, key amounts related to different Retirement Strategies have been computed. The amounts were computed using assumptions that the saving started early in your twenties and using assumptions that the saving occurred later and started in your forties. In the last activity, differences in the amounts from the different Retirement Strategies were computed, and all amounts were summarized in a Comparison Table. This activity is designed to use the Comparison Table and allow you to reflect on what you have learned and to analyze the different strategies so that some conclusions about good strategies for when and how to save for retirement can be made.

DIRECTIONS

Write a short paragraph (at least 8 sentences) explaining what lessons you have learned about saving for retirement from the activities in the Investment Project and analyzing the results as indicated below. Your paragraph should be typed and grammatically correct. Include your typed paragraph in the Investment Project results document. See Overall Presentation and Submission.

ANALYSIS PARAGRAPH CONTENT REQUIREMENTS

Your paragraph should include the following:

Identify at least two specific things you have learned.

Explain when you should start saving for retirement and why

Explain what you think is the best strategy for saving for retirement is. Be specific. Include a savings plan and how much you expect to have at retirement.

Explain why there is a difference in the amount available at retirement if you start saving later.

Explain whether or not older individuals should start saving for retirement and why you think this. What specific strategy, if any, should they use. Include a savings plan and how much they would have at retirement.

Total Possible Points 10

No Credit earned if Analysis Paragraph is handwritten. Must be typed to earn credit.

Overall (2 points)

2 points for well written, coherent paragraph with at least 8 sentences

Lessons Learned (2 points)

1 point for each explained lesson learned

When to Save (1point)

1 point for reasonable explanation of when should start saving for retirement and why. No credit without an explanation of why.

Retirement Saving Strategy (2 points)

0.5 points for proposing a reasonable strategy for saving for retirement

1.5 points for including amount to be saved and correct amount expected at retirement

Difference in Retirement Amounts (1 point)

1 point for correctly explaining why there is a difference in the amount available at retirement if you start saving later

Saving Strategy when Older (2 points)

1 point for a reasonable explanation of whether older individuals should start saving for retirement and why

1 point for a reasonable strategy for saving including amount to be saved and correct amount expected at retirement

Investment Project

NAME

Retirement Savings Strategy 1

Strategy 1: Savings Early Plan

Strategy 1: Savings Later Plan

Retirement Savings Strategy 2

Strategy 2: Savings Early Plan

Strategy 2: Savings Later Plan

3 Comparison Table of Retirement Savings Plans
(### will be actual numbers in your document)

Amount

Available at
Retirement

Amount Paid
into Retirement

Account

Amount of
Interest Earned

Strategy 1: Saving Early Plan
Invest \$250 each month starting

at age 22 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 1: Saving Later Plan
Invest \$250 each month starting

at age 42 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 22 for 15 years
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 42 for 15 years
#,###,###.## ###,###.## #,###,###.##

Differences in Strategy 1 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Strategy 2 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Saving Early Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

Differences in Saving Later Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

1A positive number means that the amount from the Saving Early plan was higher than the amount from the
Saving Later plan while a negative number means the amount from the Saving Later plan was higher.

2 A positive number means that the amount from Investment Strategy 1 was higher than the amount from
Investment Strategy 2 while a negative number means the amount from Investment Strategy 2 was higher.

4 Analysis of Retirement Savings

Insert typewritten paragraph answering all questions from this part of the project.

MATH-132Unit 2

Exam Sheet

I Prt= P = principal

1
ntr

A P
n

 
= + 

 

1

nt

A
P

r
n

=
 + 
 

I = simple interest

r = annual interest rate

rtA Pe= rt
A

P
e

= t = time or term of investment
or loan (in years)

1 1
ntr

M
n

A
r
n

   + −    =
 
 
 

1 1

nt

r
A

nM
r
n

 
 
 =

   + −    

A = future value or amount
accumulated

n = number of times interest is
compounded per year

1 1
ntr
M
n

P
r
n

−   − +    =
 
 
 

1 1
nt

r
P

nM
r
n

 
 
 =

   − +    

e = Euler’s number

M = installment payment or
monthly payment

1 1
nr

Y
n

 
= + − 
 

Y = effective annual interest
rate or effective annual yield

RETIREMENT STRATEGY 1

This activity will examine one retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete a PAM table. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 1: SAVINGS EARLY PLAN

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 1 of the Comparison Table in Part 3 of the Project.

STRATEGY 1: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2042, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 23 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 23 years, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 2 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 1

TOTAL POINTS 28

STRATEGY 1: SAVING EARLY PLAN (14 POINTS)

Question 1 Work (8 points)

5 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified

2 points – Correct substitution of values and correct answer

Question 2 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 3 Work (2 points)

1 point – Correct calculation of interest earned

Submission of picture of work in a single document (2 points)

1 point – Picture in focus & showing all work for question 1 in single pdf document for project

1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

STRATEGY 1: SAVING LATER PLAN (14 POINTS)

Question 1 Work (8 points)
5 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 3 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

RETIREMENT STRATEGY 2

This activity will examine a second retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete PAM tables. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 2: SAVINGS EARLY PLAN

Assume that you are 22 years old and are started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2022. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?

After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 3 of the Comparison Table in Part 3 of the Project.

STRATEGY 2: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2042. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?
After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 4 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 2

TOTAL POINTS 42

STRATEGY 2: SAVING EARLY PLAN (21 POINTS)

Question 1 Work (7 points)

4 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 2 Work (1 point)

1 point – Correct calculation of years left

Question 3 Work (7 points)

4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 4 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 5 Work (2 points)

1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)

1 point – Picture(s) in focus & showing all work for questions 1 and 2 in single pdf document for project

1 point – Picture(s) in focus & showing all work for questions 3, 4, and 5 in single pdf document for project

STRATEGY 2: SAVING LATER PLAN (21 POINTS)

Question 1 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (1 point)
1 point – Correct calculation of years left
Question 3 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 4 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 5 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

COMPARISON TABLE OF RETIREMENT SAVINGS PLANS

In previous activities, the amounts available at retirement, amounts paid into the retirement account, and the amount of interest earned have been computed for one or more retirement saving strategies with assumptions for starting to save when in your twenties (Saving Early plan) or for starting to save when in your forties (Saving Later plan). This activity is designed to help organize the results so the results may be analyzed, and some conclusions can be made.

DIRECTIONS

Create a Comparison Table with the results of the different Retirement Saving Plan strategies studied earlier in this project. See Retirement Strategy 1 and 2. The Comparison Table created below along with a picture of all handwritten computations needed to complete the table should be included in the Investment Project results document. See Overall Presentation and Submission.

CREATE A COMPARISON TABLE

Create a table comparing the amounts available at retirement, amount paid into the retirement account, and the amount of interest earned under the Saving Early plan and the Saving Later plan for each investment strategy. Include a brief description of the investment strategy in your table. Add footnotes to your table that clarify what is meant by a positive versus a negative number.

The Comparison Table must be created initially in a word processing program and be typed. Students will not receive credit for handwritten tables.

The first four rows of the table summarize the results from Retirement Strategy 1 and from Retirement Strategy 2.

The next four rows summarize the differences in these amounts as indicated below:

Compute and include in the table, the following columns of differences:

the difference in the amount available at retirement

the difference in the amount paid into the retirement account

the difference in the amount of interest earned

between each of the following:

the Saving Early and Saving Later plans for each investment strategy (one row for Retirement Strategy 1 and a separate row for Retirement Strategy 2)

each pair of Saving Early plans

each pair of Saving Later plans

An example of a blank Comparison Table of Retirement Savings Plans might look like the following:

Investment Project Sample Comparison Table

Total Possible Points 13

No Credit earned if Comparison Table is handwritten. Must be typed to earn credit.

Row 1 of Table (0.75 points)

0.25 point for each correct number in row

Row 2 of Table (0.75 points)

0.25 point for each correct number in row

Row 3 of Table (0.75 points)

0.25 point for each correct number in row

Row 4 of Table (0.75 points)

0.25 point for each correct number in row

Row 5 of Table (2.25 points)

0.25 point for each correct subtraction

0.5 point for each correct amount in the row

Row 6 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 7 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 8 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Included Table in single Project Results pdf document (1 points)

1 point – Included Comparison Table and picture(s) in focus & showing all subtractions in single pdf document for project

ANALYSIS OF RETIREMENT SAVINGS

In previous activities, key amounts related to different Retirement Strategies have been computed. The amounts were computed using assumptions that the saving started early in your twenties and using assumptions that the saving occurred later and started in your forties. In the last activity, differences in the amounts from the different Retirement Strategies were computed, and all amounts were summarized in a Comparison Table. This activity is designed to use the Comparison Table and allow you to reflect on what you have learned and to analyze the different strategies so that some conclusions about good strategies for when and how to save for retirement can be made.

DIRECTIONS

Write a short paragraph (at least 8 sentences) explaining what lessons you have learned about saving for retirement from the activities in the Investment Project and analyzing the results as indicated below. Your paragraph should be typed and grammatically correct. Include your typed paragraph in the Investment Project results document. See Overall Presentation and Submission.

ANALYSIS PARAGRAPH CONTENT REQUIREMENTS

Your paragraph should include the following:

Identify at least two specific things you have learned.

Explain when you should start saving for retirement and why

Explain what you think is the best strategy for saving for retirement is. Be specific. Include a savings plan and how much you expect to have at retirement.

Explain why there is a difference in the amount available at retirement if you start saving later.

Explain whether or not older individuals should start saving for retirement and why you think this. What specific strategy, if any, should they use. Include a savings plan and how much they would have at retirement.

Total Possible Points 10

No Credit earned if Analysis Paragraph is handwritten. Must be typed to earn credit.

Overall (2 points)

2 points for well written, coherent paragraph with at least 8 sentences

Lessons Learned (2 points)

1 point for each explained lesson learned

When to Save (1point)

1 point for reasonable explanation of when should start saving for retirement and why. No credit without an explanation of why.

Retirement Saving Strategy (2 points)

0.5 points for proposing a reasonable strategy for saving for retirement

1.5 points for including amount to be saved and correct amount expected at retirement

Difference in Retirement Amounts (1 point)

1 point for correctly explaining why there is a difference in the amount available at retirement if you start saving later

Saving Strategy when Older (2 points)

1 point for a reasonable explanation of whether older individuals should start saving for retirement and why

1 point for a reasonable strategy for saving including amount to be saved and correct amount expected at retirement

Investment Project

NAME

Retirement Savings Strategy 1

Strategy 1: Savings Early Plan

Strategy 1: Savings Later Plan

Retirement Savings Strategy 2

Strategy 2: Savings Early Plan

Strategy 2: Savings Later Plan

3 Comparison Table of Retirement Savings Plans
(### will be actual numbers in your document)

Amount

Available at
Retirement

Amount Paid
into Retirement

Account

Amount of
Interest Earned

Strategy 1: Saving Early Plan
Invest \$250 each month starting

at age 22 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 1: Saving Later Plan
Invest \$250 each month starting

at age 42 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 22 for 15 years
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 42 for 15 years
#,###,###.## ###,###.## #,###,###.##

Differences in Strategy 1 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Strategy 2 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Saving Early Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

Differences in Saving Later Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

1A positive number means that the amount from the Saving Early plan was higher than the amount from the
Saving Later plan while a negative number means the amount from the Saving Later plan was higher.

2 A positive number means that the amount from Investment Strategy 1 was higher than the amount from
Investment Strategy 2 while a negative number means the amount from Investment Strategy 2 was higher.

4 Analysis of Retirement Savings

Insert typewritten paragraph answering all questions from this part of the project.

MATH-132Unit 2

Exam Sheet

I Prt= P = principal

1
ntr

A P
n

 
= + 

 

1

nt

A
P

r
n

=
 + 
 

I = simple interest

r = annual interest rate

rtA Pe= rt
A

P
e

= t = time or term of investment
or loan (in years)

1 1
ntr

M
n

A
r
n

   + −    =
 
 
 

1 1

nt

r
A

nM
r
n

 
 
 =

   + −    

A = future value or amount
accumulated

n = number of times interest is
compounded per year

1 1
ntr
M
n

P
r
n

−   − +    =
 
 
 

1 1
nt

r
P

nM
r
n

 
 
 =

   − +    

e = Euler’s number

M = installment payment or
monthly payment

1 1
nr

Y
n

 
= + − 
 

Y = effective annual interest
rate or effective annual yield

RETIREMENT STRATEGY 1

This activity will examine one retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete a PAM table. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 1: SAVINGS EARLY PLAN

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 1 of the Comparison Table in Part 3 of the Project.

STRATEGY 1: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2042, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 23 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 23 years, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 2 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 1

TOTAL POINTS 28

STRATEGY 1: SAVING EARLY PLAN (14 POINTS)

Question 1 Work (8 points)

5 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified

2 points – Correct substitution of values and correct answer

Question 2 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 3 Work (2 points)

1 point – Correct calculation of interest earned

Submission of picture of work in a single document (2 points)

1 point – Picture in focus & showing all work for question 1 in single pdf document for project

1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

STRATEGY 1: SAVING LATER PLAN (14 POINTS)

Question 1 Work (8 points)
5 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 3 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

RETIREMENT STRATEGY 2

This activity will examine a second retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete PAM tables. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 2: SAVINGS EARLY PLAN

Assume that you are 22 years old and are started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2022. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?

After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 3 of the Comparison Table in Part 3 of the Project.

STRATEGY 2: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2042. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?
After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 4 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 2

TOTAL POINTS 42

STRATEGY 2: SAVING EARLY PLAN (21 POINTS)

Question 1 Work (7 points)

4 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 2 Work (1 point)

1 point – Correct calculation of years left

Question 3 Work (7 points)

4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 4 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 5 Work (2 points)

1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)

1 point – Picture(s) in focus & showing all work for questions 1 and 2 in single pdf document for project

1 point – Picture(s) in focus & showing all work for questions 3, 4, and 5 in single pdf document for project

STRATEGY 2: SAVING LATER PLAN (21 POINTS)

Question 1 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (1 point)
1 point – Correct calculation of years left
Question 3 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 4 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 5 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

COMPARISON TABLE OF RETIREMENT SAVINGS PLANS

In previous activities, the amounts available at retirement, amounts paid into the retirement account, and the amount of interest earned have been computed for one or more retirement saving strategies with assumptions for starting to save when in your twenties (Saving Early plan) or for starting to save when in your forties (Saving Later plan). This activity is designed to help organize the results so the results may be analyzed, and some conclusions can be made.

DIRECTIONS

Create a Comparison Table with the results of the different Retirement Saving Plan strategies studied earlier in this project. See Retirement Strategy 1 and 2. The Comparison Table created below along with a picture of all handwritten computations needed to complete the table should be included in the Investment Project results document. See Overall Presentation and Submission.

CREATE A COMPARISON TABLE

Create a table comparing the amounts available at retirement, amount paid into the retirement account, and the amount of interest earned under the Saving Early plan and the Saving Later plan for each investment strategy. Include a brief description of the investment strategy in your table. Add footnotes to your table that clarify what is meant by a positive versus a negative number.

The Comparison Table must be created initially in a word processing program and be typed. Students will not receive credit for handwritten tables.

The first four rows of the table summarize the results from Retirement Strategy 1 and from Retirement Strategy 2.

The next four rows summarize the differences in these amounts as indicated below:

Compute and include in the table, the following columns of differences:

the difference in the amount available at retirement

the difference in the amount paid into the retirement account

the difference in the amount of interest earned

between each of the following:

the Saving Early and Saving Later plans for each investment strategy (one row for Retirement Strategy 1 and a separate row for Retirement Strategy 2)

each pair of Saving Early plans

each pair of Saving Later plans

An example of a blank Comparison Table of Retirement Savings Plans might look like the following:

Investment Project Sample Comparison Table

Total Possible Points 13

No Credit earned if Comparison Table is handwritten. Must be typed to earn credit.

Row 1 of Table (0.75 points)

0.25 point for each correct number in row

Row 2 of Table (0.75 points)

0.25 point for each correct number in row

Row 3 of Table (0.75 points)

0.25 point for each correct number in row

Row 4 of Table (0.75 points)

0.25 point for each correct number in row

Row 5 of Table (2.25 points)

0.25 point for each correct subtraction

0.5 point for each correct amount in the row

Row 6 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 7 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 8 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Included Table in single Project Results pdf document (1 points)

1 point – Included Comparison Table and picture(s) in focus & showing all subtractions in single pdf document for project

ANALYSIS OF RETIREMENT SAVINGS

In previous activities, key amounts related to different Retirement Strategies have been computed. The amounts were computed using assumptions that the saving started early in your twenties and using assumptions that the saving occurred later and started in your forties. In the last activity, differences in the amounts from the different Retirement Strategies were computed, and all amounts were summarized in a Comparison Table. This activity is designed to use the Comparison Table and allow you to reflect on what you have learned and to analyze the different strategies so that some conclusions about good strategies for when and how to save for retirement can be made.

DIRECTIONS

Write a short paragraph (at least 8 sentences) explaining what lessons you have learned about saving for retirement from the activities in the Investment Project and analyzing the results as indicated below. Your paragraph should be typed and grammatically correct. Include your typed paragraph in the Investment Project results document. See Overall Presentation and Submission.

ANALYSIS PARAGRAPH CONTENT REQUIREMENTS

Your paragraph should include the following:

Identify at least two specific things you have learned.

Explain when you should start saving for retirement and why

Explain what you think is the best strategy for saving for retirement is. Be specific. Include a savings plan and how much you expect to have at retirement.

Explain why there is a difference in the amount available at retirement if you start saving later.

Explain whether or not older individuals should start saving for retirement and why you think this. What specific strategy, if any, should they use. Include a savings plan and how much they would have at retirement.

Total Possible Points 10

No Credit earned if Analysis Paragraph is handwritten. Must be typed to earn credit.

Overall (2 points)

2 points for well written, coherent paragraph with at least 8 sentences

Lessons Learned (2 points)

1 point for each explained lesson learned

When to Save (1point)

1 point for reasonable explanation of when should start saving for retirement and why. No credit without an explanation of why.

Retirement Saving Strategy (2 points)

0.5 points for proposing a reasonable strategy for saving for retirement

1.5 points for including amount to be saved and correct amount expected at retirement

Difference in Retirement Amounts (1 point)

1 point for correctly explaining why there is a difference in the amount available at retirement if you start saving later

Saving Strategy when Older (2 points)

1 point for a reasonable explanation of whether older individuals should start saving for retirement and why

1 point for a reasonable strategy for saving including amount to be saved and correct amount expected at retirement

Investment Project

NAME

Retirement Savings Strategy 1

Strategy 1: Savings Early Plan

Strategy 1: Savings Later Plan

Retirement Savings Strategy 2

Strategy 2: Savings Early Plan

Strategy 2: Savings Later Plan

3 Comparison Table of Retirement Savings Plans
(### will be actual numbers in your document)

Amount

Available at
Retirement

Amount Paid
into Retirement

Account

Amount of
Interest Earned

Strategy 1: Saving Early Plan
Invest \$250 each month starting

at age 22 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 1: Saving Later Plan
Invest \$250 each month starting

at age 42 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 22 for 15 years
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 42 for 15 years
#,###,###.## ###,###.## #,###,###.##

Differences in Strategy 1 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Strategy 2 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Saving Early Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

Differences in Saving Later Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

1A positive number means that the amount from the Saving Early plan was higher than the amount from the
Saving Later plan while a negative number means the amount from the Saving Later plan was higher.

2 A positive number means that the amount from Investment Strategy 1 was higher than the amount from
Investment Strategy 2 while a negative number means the amount from Investment Strategy 2 was higher.

4 Analysis of Retirement Savings

Insert typewritten paragraph answering all questions from this part of the project.

MATH-132Unit 2

Exam Sheet

I Prt= P = principal

1
ntr

A P
n

 
= + 

 

1

nt

A
P

r
n

=
 + 
 

I = simple interest

r = annual interest rate

rtA Pe= rt
A

P
e

= t = time or term of investment
or loan (in years)

1 1
ntr

M
n

A
r
n

   + −    =
 
 
 

1 1

nt

r
A

nM
r
n

 
 
 =

   + −    

A = future value or amount
accumulated

n = number of times interest is
compounded per year

1 1
ntr
M
n

P
r
n

−   − +    =
 
 
 

1 1
nt

r
P

nM
r
n

 
 
 =

   − +    

e = Euler’s number

M = installment payment or
monthly payment

1 1
nr

Y
n

 
= + − 
 

Y = effective annual interest
rate or effective annual yield

RETIREMENT STRATEGY 1

This activity will examine one retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete a PAM table. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 1: SAVINGS EARLY PLAN

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 1 of the Comparison Table in Part 3 of the Project.

STRATEGY 1: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2042, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 23 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 23 years, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 2 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 1

TOTAL POINTS 28

STRATEGY 1: SAVING EARLY PLAN (14 POINTS)

Question 1 Work (8 points)

5 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified

2 points – Correct substitution of values and correct answer

Question 2 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 3 Work (2 points)

1 point – Correct calculation of interest earned

Submission of picture of work in a single document (2 points)

1 point – Picture in focus & showing all work for question 1 in single pdf document for project

1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

STRATEGY 1: SAVING LATER PLAN (14 POINTS)

Question 1 Work (8 points)
5 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 3 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

RETIREMENT STRATEGY 2

This activity will examine a second retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete PAM tables. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 2: SAVINGS EARLY PLAN

Assume that you are 22 years old and are started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2022. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?

After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 3 of the Comparison Table in Part 3 of the Project.

STRATEGY 2: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2042. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?
After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 4 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 2

TOTAL POINTS 42

STRATEGY 2: SAVING EARLY PLAN (21 POINTS)

Question 1 Work (7 points)

4 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 2 Work (1 point)

1 point – Correct calculation of years left

Question 3 Work (7 points)

4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 4 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 5 Work (2 points)

1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)

1 point – Picture(s) in focus & showing all work for questions 1 and 2 in single pdf document for project

1 point – Picture(s) in focus & showing all work for questions 3, 4, and 5 in single pdf document for project

STRATEGY 2: SAVING LATER PLAN (21 POINTS)

Question 1 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (1 point)
1 point – Correct calculation of years left
Question 3 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 4 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 5 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

COMPARISON TABLE OF RETIREMENT SAVINGS PLANS

In previous activities, the amounts available at retirement, amounts paid into the retirement account, and the amount of interest earned have been computed for one or more retirement saving strategies with assumptions for starting to save when in your twenties (Saving Early plan) or for starting to save when in your forties (Saving Later plan). This activity is designed to help organize the results so the results may be analyzed, and some conclusions can be made.

DIRECTIONS

Create a Comparison Table with the results of the different Retirement Saving Plan strategies studied earlier in this project. See Retirement Strategy 1 and 2. The Comparison Table created below along with a picture of all handwritten computations needed to complete the table should be included in the Investment Project results document. See Overall Presentation and Submission.

CREATE A COMPARISON TABLE

Create a table comparing the amounts available at retirement, amount paid into the retirement account, and the amount of interest earned under the Saving Early plan and the Saving Later plan for each investment strategy. Include a brief description of the investment strategy in your table. Add footnotes to your table that clarify what is meant by a positive versus a negative number.

The Comparison Table must be created initially in a word processing program and be typed. Students will not receive credit for handwritten tables.

The first four rows of the table summarize the results from Retirement Strategy 1 and from Retirement Strategy 2.

The next four rows summarize the differences in these amounts as indicated below:

Compute and include in the table, the following columns of differences:

the difference in the amount available at retirement

the difference in the amount paid into the retirement account

the difference in the amount of interest earned

between each of the following:

the Saving Early and Saving Later plans for each investment strategy (one row for Retirement Strategy 1 and a separate row for Retirement Strategy 2)

each pair of Saving Early plans

each pair of Saving Later plans

An example of a blank Comparison Table of Retirement Savings Plans might look like the following:

Investment Project Sample Comparison Table

Total Possible Points 13

No Credit earned if Comparison Table is handwritten. Must be typed to earn credit.

Row 1 of Table (0.75 points)

0.25 point for each correct number in row

Row 2 of Table (0.75 points)

0.25 point for each correct number in row

Row 3 of Table (0.75 points)

0.25 point for each correct number in row

Row 4 of Table (0.75 points)

0.25 point for each correct number in row

Row 5 of Table (2.25 points)

0.25 point for each correct subtraction

0.5 point for each correct amount in the row

Row 6 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 7 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 8 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Included Table in single Project Results pdf document (1 points)

1 point – Included Comparison Table and picture(s) in focus & showing all subtractions in single pdf document for project

ANALYSIS OF RETIREMENT SAVINGS

In previous activities, key amounts related to different Retirement Strategies have been computed. The amounts were computed using assumptions that the saving started early in your twenties and using assumptions that the saving occurred later and started in your forties. In the last activity, differences in the amounts from the different Retirement Strategies were computed, and all amounts were summarized in a Comparison Table. This activity is designed to use the Comparison Table and allow you to reflect on what you have learned and to analyze the different strategies so that some conclusions about good strategies for when and how to save for retirement can be made.

DIRECTIONS

Write a short paragraph (at least 8 sentences) explaining what lessons you have learned about saving for retirement from the activities in the Investment Project and analyzing the results as indicated below. Your paragraph should be typed and grammatically correct. Include your typed paragraph in the Investment Project results document. See Overall Presentation and Submission.

ANALYSIS PARAGRAPH CONTENT REQUIREMENTS

Your paragraph should include the following:

Identify at least two specific things you have learned.

Explain when you should start saving for retirement and why

Explain what you think is the best strategy for saving for retirement is. Be specific. Include a savings plan and how much you expect to have at retirement.

Explain why there is a difference in the amount available at retirement if you start saving later.

Explain whether or not older individuals should start saving for retirement and why you think this. What specific strategy, if any, should they use. Include a savings plan and how much they would have at retirement.

Total Possible Points 10

No Credit earned if Analysis Paragraph is handwritten. Must be typed to earn credit.

Overall (2 points)

2 points for well written, coherent paragraph with at least 8 sentences

Lessons Learned (2 points)

1 point for each explained lesson learned

When to Save (1point)

1 point for reasonable explanation of when should start saving for retirement and why. No credit without an explanation of why.

Retirement Saving Strategy (2 points)

0.5 points for proposing a reasonable strategy for saving for retirement

1.5 points for including amount to be saved and correct amount expected at retirement

Difference in Retirement Amounts (1 point)

1 point for correctly explaining why there is a difference in the amount available at retirement if you start saving later

Saving Strategy when Older (2 points)

1 point for a reasonable explanation of whether older individuals should start saving for retirement and why

1 point for a reasonable strategy for saving including amount to be saved and correct amount expected at retirement

Investment Project

NAME

Retirement Savings Strategy 1

Strategy 1: Savings Early Plan

Strategy 1: Savings Later Plan

Retirement Savings Strategy 2

Strategy 2: Savings Early Plan

Strategy 2: Savings Later Plan

3 Comparison Table of Retirement Savings Plans
(### will be actual numbers in your document)

Amount

Available at
Retirement

Amount Paid
into Retirement

Account

Amount of
Interest Earned

Strategy 1: Saving Early Plan
Invest \$250 each month starting

at age 22 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 1: Saving Later Plan
Invest \$250 each month starting

at age 42 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 22 for 15 years
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 42 for 15 years
#,###,###.## ###,###.## #,###,###.##

Differences in Strategy 1 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Strategy 2 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Saving Early Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

Differences in Saving Later Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

1A positive number means that the amount from the Saving Early plan was higher than the amount from the
Saving Later plan while a negative number means the amount from the Saving Later plan was higher.

2 A positive number means that the amount from Investment Strategy 1 was higher than the amount from
Investment Strategy 2 while a negative number means the amount from Investment Strategy 2 was higher.

4 Analysis of Retirement Savings

Insert typewritten paragraph answering all questions from this part of the project.

MATH-132Unit 2

Exam Sheet

I Prt= P = principal

1
ntr

A P
n

 
= + 

 

1

nt

A
P

r
n

=
 + 
 

I = simple interest

r = annual interest rate

rtA Pe= rt
A

P
e

= t = time or term of investment
or loan (in years)

1 1
ntr

M
n

A
r
n

   + −    =
 
 
 

1 1

nt

r
A

nM
r
n

 
 
 =

   + −    

A = future value or amount
accumulated

n = number of times interest is
compounded per year

1 1
ntr
M
n

P
r
n

−   − +    =
 
 
 

1 1
nt

r
P

nM
r
n

 
 
 =

   − +    

e = Euler’s number

M = installment payment or
monthly payment

1 1
nr

Y
n

 
= + − 
 

Y = effective annual interest
rate or effective annual yield

RETIREMENT STRATEGY 1

This activity will examine one retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete a PAM table. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 1: SAVINGS EARLY PLAN

Assume that you are 22 years old and started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2022, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 43 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 43 years, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 1 of the Comparison Table in Part 3 of the Project.

STRATEGY 1: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$250 at the end of each month into a retirement account paying 8.75% compounded monthly from January 1, 2042, until you retire. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 23 years, how much did you pay into your retirement account?

Assuming you made all the monthly payments for 23 years, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 2 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 1

TOTAL POINTS 28

STRATEGY 1: SAVING EARLY PLAN (14 POINTS)

Question 1 Work (8 points)

5 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified

2 points – Correct substitution of values and correct answer

Question 2 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 3 Work (2 points)

1 point – Correct calculation of interest earned

Submission of picture of work in a single document (2 points)

1 point – Picture in focus & showing all work for question 1 in single pdf document for project

1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

STRATEGY 1: SAVING LATER PLAN (14 POINTS)

Question 1 Work (8 points)
5 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 3 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

RETIREMENT STRATEGY 2

This activity will examine a second retirement savings strategy and examine how this strategy is affected by the length of time the strategy is used.

DIRECTIONS

Solve each of the problems below. Complete PAM tables. Identify the best formula to answer the question. Substitute values into your formula and show your answer. In short, show all your work to earn full credit. All answers will be rounded to dollars and cents. Work should be handwritten. Submit a picture of your handwritten work for all questions and parts of the project in a single document. See instructions for Overall Presentation and Submission.

STRATEGY 2: SAVINGS EARLY PLAN

Assume that you are 22 years old and are started saving for retirement on January 1, 2022. You plan to retire on December 31, 2064, when you are 64 years old. There are 43 years from the time you started investing (saving) until you retire. You have no previous or other retirement savings when you start to save. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2022. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?

After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 43 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 43 years?

Enter the amounts from this strategy in Row 3 of the Comparison Table in Part 3 of the Project.

STRATEGY 2: SAVINGS LATER PLAN

Assume that you are 22 years old but decide to wait before saving for retirement. You decide to start saving later when you are 42 years old. As a result, you start saving on January 1, 2042. You plan to retire on December 31, 2064, when you are 64 years old. There are 23 years from the time you started investing (saving) until you retire. When you start investing in 2042, you have no previous or other retirement savings. Assume there are 365 days in each year from 2022 to 2064. (Ignore leap years). Assume that taxes will not affect any of the amounts or your savings.

You invest \$350 at the end of each month into a retirement account paying 8.75% compounded monthly for 15 years starting on January 1, 2042. After 15 years, you do not make any more payments or withdrawals and leave the money in the retirement account until retirement. Show all work and answer the following questions:

Assuming no withdrawals or additional payments were made, how much money will be in your retirement account after 15 years?
After 15 years, how many years are left until you retire?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much money will be in your retirement account after 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much did you pay into your retirement account over the 23 years?

Assuming you made all the monthly payments for 15 years and left the money in the account without making any additional payments or withdrawals, how much interest did you earn over the 23 years?

Enter the amounts from this strategy in Row 4 of the Comparison Table in Part 3 of the Project.

GRADING RUBRIC FOR RETIREMENT STRATEGY 2

TOTAL POINTS 42

STRATEGY 2: SAVING EARLY PLAN (21 POINTS)

Question 1 Work (7 points)

4 points – Table of values with correct value for (PAM Table)

1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 2 Work (1 point)

1 point – Correct calculation of years left

Question 3 Work (7 points)

4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer

Question 4 Work (2 points)

1 point – Correct calculation of amount paid into retirement account

Question 5 Work (2 points)

1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)

1 point – Picture(s) in focus & showing all work for questions 1 and 2 in single pdf document for project

1 point – Picture(s) in focus & showing all work for questions 3, 4, and 5 in single pdf document for project

STRATEGY 2: SAVING LATER PLAN (21 POINTS)

Question 1 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 2 Work (1 point)
1 point – Correct calculation of years left
Question 3 Work (7 points)
4 points – Table of values with correct value for (PAM Table)
1 point – Correct Formula identified
2 points – Correct substitution of values and correct answer
Question 4 Work (2 points)
1 point – Correct calculation of amount paid into retirement account
Question 5 Work (2 points)
1 point – Correct calculation of interest earned
Submission of picture of work in a single document (2 points)
1 point – Picture in focus & showing all work for question 1 in single pdf document for project
1 point – Picture in focus & showing all work for questions 2 and 3 in single pdf document for project

COMPARISON TABLE OF RETIREMENT SAVINGS PLANS

In previous activities, the amounts available at retirement, amounts paid into the retirement account, and the amount of interest earned have been computed for one or more retirement saving strategies with assumptions for starting to save when in your twenties (Saving Early plan) or for starting to save when in your forties (Saving Later plan). This activity is designed to help organize the results so the results may be analyzed, and some conclusions can be made.

DIRECTIONS

Create a Comparison Table with the results of the different Retirement Saving Plan strategies studied earlier in this project. See Retirement Strategy 1 and 2. The Comparison Table created below along with a picture of all handwritten computations needed to complete the table should be included in the Investment Project results document. See Overall Presentation and Submission.

CREATE A COMPARISON TABLE

Create a table comparing the amounts available at retirement, amount paid into the retirement account, and the amount of interest earned under the Saving Early plan and the Saving Later plan for each investment strategy. Include a brief description of the investment strategy in your table. Add footnotes to your table that clarify what is meant by a positive versus a negative number.

The Comparison Table must be created initially in a word processing program and be typed. Students will not receive credit for handwritten tables.

The first four rows of the table summarize the results from Retirement Strategy 1 and from Retirement Strategy 2.

The next four rows summarize the differences in these amounts as indicated below:

Compute and include in the table, the following columns of differences:

the difference in the amount available at retirement

the difference in the amount paid into the retirement account

the difference in the amount of interest earned

between each of the following:

the Saving Early and Saving Later plans for each investment strategy (one row for Retirement Strategy 1 and a separate row for Retirement Strategy 2)

each pair of Saving Early plans

each pair of Saving Later plans

An example of a blank Comparison Table of Retirement Savings Plans might look like the following:

Investment Project Sample Comparison Table

Total Possible Points 13

No Credit earned if Comparison Table is handwritten. Must be typed to earn credit.

Row 1 of Table (0.75 points)

0.25 point for each correct number in row

Row 2 of Table (0.75 points)

0.25 point for each correct number in row

Row 3 of Table (0.75 points)

0.25 point for each correct number in row

Row 4 of Table (0.75 points)

0.25 point for each correct number in row

Row 5 of Table (2.25 points)

0.25 point for each correct subtraction

0.5 point for each correct amount in the row

Row 6 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 7 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Row 8 of Table (2.25 points)

0.25 point for each correct subtraction
0.5 point for each correct amount in the row

Included Table in single Project Results pdf document (1 points)

1 point – Included Comparison Table and picture(s) in focus & showing all subtractions in single pdf document for project

ANALYSIS OF RETIREMENT SAVINGS

In previous activities, key amounts related to different Retirement Strategies have been computed. The amounts were computed using assumptions that the saving started early in your twenties and using assumptions that the saving occurred later and started in your forties. In the last activity, differences in the amounts from the different Retirement Strategies were computed, and all amounts were summarized in a Comparison Table. This activity is designed to use the Comparison Table and allow you to reflect on what you have learned and to analyze the different strategies so that some conclusions about good strategies for when and how to save for retirement can be made.

DIRECTIONS

Write a short paragraph (at least 8 sentences) explaining what lessons you have learned about saving for retirement from the activities in the Investment Project and analyzing the results as indicated below. Your paragraph should be typed and grammatically correct. Include your typed paragraph in the Investment Project results document. See Overall Presentation and Submission.

ANALYSIS PARAGRAPH CONTENT REQUIREMENTS

Your paragraph should include the following:

Identify at least two specific things you have learned.

Explain when you should start saving for retirement and why

Explain what you think is the best strategy for saving for retirement is. Be specific. Include a savings plan and how much you expect to have at retirement.

Explain why there is a difference in the amount available at retirement if you start saving later.

Explain whether or not older individuals should start saving for retirement and why you think this. What specific strategy, if any, should they use. Include a savings plan and how much they would have at retirement.

Total Possible Points 10

No Credit earned if Analysis Paragraph is handwritten. Must be typed to earn credit.

Overall (2 points)

2 points for well written, coherent paragraph with at least 8 sentences

Lessons Learned (2 points)

1 point for each explained lesson learned

When to Save (1point)

1 point for reasonable explanation of when should start saving for retirement and why. No credit without an explanation of why.

Retirement Saving Strategy (2 points)

0.5 points for proposing a reasonable strategy for saving for retirement

1.5 points for including amount to be saved and correct amount expected at retirement

Difference in Retirement Amounts (1 point)

1 point for correctly explaining why there is a difference in the amount available at retirement if you start saving later

Saving Strategy when Older (2 points)

1 point for a reasonable explanation of whether older individuals should start saving for retirement and why

1 point for a reasonable strategy for saving including amount to be saved and correct amount expected at retirement

Investment Project

NAME

Retirement Savings Strategy 1

Strategy 1: Savings Early Plan

Strategy 1: Savings Later Plan

Retirement Savings Strategy 2

Strategy 2: Savings Early Plan

Strategy 2: Savings Later Plan

3 Comparison Table of Retirement Savings Plans
(### will be actual numbers in your document)

Amount

Available at
Retirement

Amount Paid
into Retirement

Account

Amount of
Interest Earned

Strategy 1: Saving Early Plan
Invest \$250 each month starting

at age 22 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 1: Saving Later Plan
Invest \$250 each month starting

at age 42 until retirement
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 22 for 15 years
#,###,###.## ###,###.## #,###,###.##

Strategy 2: Saving Early Plan
Invest \$350 each month starting

at age 42 for 15 years
#,###,###.## ###,###.## #,###,###.##

Differences in Strategy 1 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Strategy 2 between
Saving Early and Saving Later

Plans1
###,###.## ###,###.## ###,###.##

Differences in Saving Early Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

Differences in Saving Later Plans
between Strategy 1 and 22 ###,###.## ###,###.## ###,###.##

1A positive number means that the amount from the Saving Early plan was higher than the amount from the
Saving Later plan while a negative number means the amount from the Saving Later plan was higher.

2 A positive number means that the amount from Investment Strategy 1 was higher than the amount from
Investment Strategy 2 while a negative number means the amount from Investment Strategy 2 was higher.

4 Analysis of Retirement Savings

Insert typewritten paragraph answering all questions from this part of the project.

MATH-132Unit 2

Exam Sheet

I Prt= P = principal

1
ntr

A P
n

 
= + 

 

1

nt

A
P

r
n

=
 + 
 

I = simple interest

r = annual interest rate

rtA Pe= rt
A

P
e

= t = time or term of investment
or loan (in years)

1 1
ntr

M
n

A
r
n

   + −    =
 
 
 

1 1

nt

r
A

nM
r
n

 
 
 =

   + −    

A = future value or amount
accumulated

n = number of times interest is
compounded per year

1 1
ntr
M
n

P
r
n

−   − +    =
 
 
 

1 1
nt

r
P

nM
r
n

 
 
 =

   − +    

e = Euler’s number

M = installment payment or
monthly payment

1 1
nr

Y
n

 
= + − 
 

Y = effective annual interest
rate or effective annual yield

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