Currently in August, 2017), Abby wants to have $20,000 available in August 2021 to make a college tuition payment. To be able to have this amount available, Abby will make equal annual deposits in an investment account earning 12% annually in August 2017,2018,2019,2020,and 2021. What is the annual amount to be deposited?
A) $5,548
B) $4,000
C) $3,148
D) $2,270

Question

Quizplus · Accepted Answer

To solve this, 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 ($20,000), $P$ is the annual payment, $r$ is the annual interest rate (12% or 0.12), and $n$ is the number of payments (5). Rearranging the formula to solve for $P$ gives us $P = FV / \left( \frac{(1 + r)^n - 1}{r} \right)$. Plugging in the values gives $P = 20,000 / \left( \frac{(1 + 0.12)^5 - 1}{0.12} \right)$, which calculates to approximately $3,148.

Currently in August, 2017), Abby Wants to Have $20,000 Available