Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,000 deposits at the end of each of the next 15 years. If the annual interest rate is 8%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Round your answer to the nearest cent.
A) $79,790.73
B) $73,880.30
C) $68,407.69
D) $63,340.45
E) $93,067.90

Question

Suppose that Bob delays starting an IRA for the first 10 years he works but then makes $2,000 deposits at the end of each of the next 15 years. If the annual interest rate is 8%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Round your answer to the nearest cent. ​
A) $79,790.73
B) $73,880.30
C) $68,407.69
D) $63,340.45
E) $93,067.90

Quizplus · Accepted Answer

The total amount in the IRA can be calculated using the future value of an annuity formula for the 15 years of deposits, plus the future value of a single sum for the 5 additional years without deposits. The formula for the future value of an annuity is $FV = P \times \frac{(1 + r)^n - 1}{r}$, where $P$ is the payment amount, $r$ is the annual interest rate, and $n$ is the number of periods. For the 15 years of deposits, $P = 2000$, $r = 0.08$, and $n = 15$, so $FV = 2000 \times \frac{(1 + 0.08)^{15} - 1}{0.08} = 2000 \times 27.1525 = 54305$. For the next 5 years without additional deposits, the future value of this amount can be calculated using the formula for the future value of a single sum, $FV = PV \times (1 + r)^n$, where $PV$ is the present value. Here, $PV = 54305$, $r = 0.08$, and $n = 5$, so $FV = 54305 \times (1 + 0.08)^5 = 54305 \times 1.469328 = 79790.73$. Therefore, the total amount in the account at the end of the 30-year period is approximately $79,790.73.

Suppose That Bob Delays Starting an IRA for the First