Finance Management

The Time Value of Money

Mary is ready to retire however before she does she wants to address the following financial issues, which she is seeking assistance in doing so:

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?

In order to determine how much Mary’s savings account will be worth after making her last deposit a year from now the future value of an annuity formula will need to be utilized. The equation which will allow us to calculate the correct answer is:

FVA = A * FVIFA (n=20, i = 5%)

FVA = $500 x 33.033

FVA = 16,533

The total amount Mary’s savings account will be worth is $16,533.

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 way to calculate how much the one-time payment would amount to the present value of an annuity formula must be used. The following equation will help to reach the correct answer:

PVA = A * PVIFA (n = 20, i = 7%)

PVA = $75,000 x 10.594

PVA = $794,550

If Mary were to receive a one-time payment the day after she retires she would receive $794,550. However, if she took the $75,000 a year for 20 years it would equal $1,500,000.

Issue C:

Mary’s replacement is unexpectedly hired away by another school, and Mary is asked to stay in her position for another three years. The board assumes the bonus should stay...