Currently on January 1, 2017), Nolan wants to have $45,000 available on December 31 2022 to purchase a luxury car. To be able to have this amount available, Nolan will make equal quarterly deposits for the next six years in an investment account earning a 16% annual return compounded quarterly. Nolan will make these deposits at the end of March, June, September, and December. What is the amount to be deposited quarterly for the next six years that will provide for a $45,000 balance at the end of 2022?
A) $1,875
B) $1,253
C) $1,151
D) $210

Question

Quizplus · Accepted Answer

To solve this problem, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value of the annuity, $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. Given that the annual interest rate is 16% compounded quarterly, the quarterly interest rate is $16\% / 4 = 4\%$, or $0.04$ as a decimal. The total number of quarterly deposits over six years is $6 \times 4 = 24$. We want the future value ($FV$) to be $45,000. Rearranging the formula to solve for $P$ gives us $P = FV / \left( \frac{(1 + r)^n - 1}{r} \right)$. Substituting the given values, we get $P = 45,000 / \left( \frac{(1 + 0.04)^{24} - 1}{0.04} \right)$, which calculates to approximately $1,151. Therefore, Nolan needs to deposit about $1,151 quarterly.

Currently on January 1, 2017), Nolan Wants to Have $45,000