Larry wants to start an IRA that will have $ 400,000 in it when he retires in 22 years. How much should he invest semiannually in his IRA to do this if the interest is 9% compounded semiannually?
A) $ 3019.28
B) $ 11,018.26
C) $ 3032.28
D) $ 2889.93

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the future value of an annuity: $FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right)$, where $FV$ is the future value, $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Here, $FV = \$400,000$, $r = \frac{0.09}{2} = 0.045$ (since the interest is compounded semiannually), and $n = 22 \times 2 = 44$ (because payments are made semiannually for 22 years). Rearranging the formula to solve for $P$ gives us $P = \frac{FV}{\left(\frac{(1 + r)^n - 1}{r}\right)}$. Plugging in the values, we get $P = \frac{400,000}{\left(\frac{(1 + 0.045)^{44} - 1}{0.045}\right)}$, which calculates to approximately \$3032.28.

Larry Wants to Start an IRA That Will Have