Question

Shaylea, age 22, just started working full time and plans to deposit $5500 annually into an IRA earning 7 percent interest compounded annually. Deposits will be made at the end of each year. How much would she have in 20 years, 30 years, and 40 years? If she changed her investment period and instead invested $458.33 monthly and the investment also changed to monthly compounding, how much would she have after the same three time periods? Comment on the differences over time below.

For the following: round to the nearest cent

-With annual investments and compounding, after 20 years, she would have ______?

-With annual investments and compounding, after 30 years, she would have ______?

-With annual investments and compounding, after 40 years, she would have ______?

-With monthly investments and monthly compounding, after 20 years, she would have ______?

-With monthly investments and monthly compounding, after 30 years, she would have ______?

-With monthly investments and monthly compounding, after 40 years, she would have ______?

The differences are (select the best choice below)

a. The longer the money is invest, the more you will have in the future. The number of compounding periods does not have any effect on the investment

b. the longer the money is invested, the more you will have in the future. The more compounding periods you have in a given time, the more money you will have in the future

c. the longer the money is invested, the less you will have in the future because the interest rate does not change with the cost of living

d. the longer the money is invested the more you will have in the future. The more compounding periods you have, the less money you will have in the future because the interest rate is lower

Answer 1

Amount available at the end of the specified period is calculated using the FV function of Excel.

Results are as follows:

With annual investments and compounding, after 20 years, she would have $225,475.21

With annual investments and compounding, after 30 years, she would have $519,534.32

With annual investments and compounding, after 40 years, she would have $1,097,993.12

With monthly investments and monthly compounding, after 20 years, she would have $238,756.32

With monthly investments and monthly compounding, after 30 years, she would have $559,149.31

With monthly investments and monthly compounding, after 40 years, she would have $1,203,030.72

Regarding the differences, the answer is option (b) of the set given, as follows:

"The longer the money is invested, the more you will have in the future. The more compounding periods you have in a given time, the more money you will have in the future".

Details of calculation under various prescriptions are as follows, with a sample of cell reference.