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)?
A) $48,359
B) $35,967
C) $48,000
D) $55,340

Question

Quizplus · Accepted Answer

To find the future value of the annuity payments at the end of Year 25, we first calculate the future value of the annuity at the end of Year 10 using the future value of an annuity formula, and then we calculate the future value of this amount at the end of Year 25 by applying the future value of a single sum formula.1. Future value of the annuity at the end of Year 10:$$FV_{annuity} = P \times \frac{(1 + r)^n - 1}{r}$$Where:- $P = \$1000$ (annual payment),- $r = 0.09$ (interest rate),- $n = 10$ (number of payments).$$FV_{annuity} = \$1000 \times \frac{(1 + 0.09)^{10} - 1}{0.09}$$$$FV_{annuity} = \$1000 \times \frac{(1.09)^{10} - 1}{0.09}$$$$FV_{annuity} = \$1000 \times \frac{2.367364 - 1}{0.09}$$$$FV_{annuity} = \$1000 \times 15.20404$$$$FV_{annuity} = \$15,204.04$$2. Future value of this amount at the end of Year 25:$$FV = PV \times (1 + r)^n$$Where:- $PV = \$15,204.04$ (the amount at the end of Year 10),- $r = 0.09$ (interest rate),- $n = 15$ (the number of years from Year 10 to Year 25).$$FV = \$15,204.04 \times (1 + 0.09)^{15}$$$$FV = \$15,204.04 \times (1.09)^{15}$$$$FV = \$15,204.04 \times 3.642094$$$$FV = \$55,340.10$$Rounded to the nearest dollar, the value in the account at the end of Year 25 is approximately $55,340.

Assume You Are to Receive a 10-Year Annuity with Annual