The Time Value of Money

The Time Value of Money

Cari Nelson

Argosy University Phoenix

The Time Value of Money

Mary has been working for a university for almost 25 years and is now approaching retirement. She wants to address several financial issues before her retirement and has asked you to help her resolve the situations below. Her assignment to you is to provide a 4-5 page report, addressing each of the following issues separately. You are to show all your calculations and provide a detailed explanation for each issue.

Issue A:

For the last 19 years, Mary has been depositing $500 in her savings account , which has earned 5% per year, compounded annually and is expected to continue paying that amount. Mary will make one more $500 deposit one year from today. If Mary closes the account right after she makes the last deposit, how much will this account be worth at that time?

Issue A:

Until now Mary has made 19 deposits into her savings account. When she makes her last deposit its value will be $500.00. Her second last deposit would then be a year old and have future value 500*(1+5%). Her third last deposit would be of value 500*(1+5%)^2. If we include her first deposit it would be valued at 500*(1+5%)^19. To break it down;

>500+500**1.05+500*1.05^2…..+50*1.05^19

>500(1.05^20-1)(1.05-1)

>16532.98

If Mary closes her account right after she makes the last deposit it will be worth $16532.98.

Issue B:

Mary has been working at the university for 25 years, with an excellent record of service. As a result, the board wants to reward her with a bonus to her retirement package. They are offering her $75,000 a year for 20 years, starting one year from her retirement date and each year for 19 years after that date. Mary would prefer a one-time payment the day after she retires. What would this amount be if the appropriate interest rate is 7%?

The future value of 20 payments of $75,000 at the end of each year for 20 years at 7%/yr is: 

fv = pmt * ((1+r) ^ t) - 1) /...