Assume you are to receive a 10-year annuity with annual payments of $1000. The f
ID: 2776422 • Letter: A
Question
Assume you are to receive a 10-year annuity with annual payments of $1000. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 10. You will invest each payment in an account that pays 9 percent compounded annually. Although the annuity payments stop at the end of year 10, you will not withdraw any money from the account until 25 years from today, and the account will continue to earn 9% for the entire 25-year period. What will be the value in your account at the end of Year 25 (rounded to the nearest dollar)?
Select one:
a. $48,000
b. $55,340
c. $48,359
d. $35,967
Explanation / Answer
Value in the account at the end of 25th year = $ 55,340
Amount received at the end of Year A = $ 1000
Period for which amount is received n = 10 years
This amount is invested at r = 9% compounded annually.
That is the investment is made at the beginning of the period (or annuity due).
Future value of Annuity due P1= (1+r) * A * [((1+r)^n-1-1)/r)
= (1+0.09) * 1000 * [((1+0.09)^10) -1)/0.09]
= 1.09 * 1000 * [(2.367364 -1)/0.09]
= 1090 * (1.367364/0.09)
= 1090 * 15.19293 = $ 16,560.297 or $ 16,560.30 (rounded off)
This amount is further invested for a period of 25-11 = 14 years as the money is received at the end of year 10 or beginning of the year 11 and value is received end of year 25.
Future value of the accumulated amount above P2 = $ 16560.30 * (1+0.09)^14
= $ 16560.30 * 3.341727
= $ 55,340.00
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