Jessie's Dry Cleaner began making $2,000 equal, annual deposits in a fund starting on January 2, 2016. The fund earns 10% compounded annually, and the last deposit is made on January 2, 2020. How much will be in the fund on January 2, 2021, one year after the final deposit?
A) $15,000
B) $13,431
C) $12,105
D) $10,641

Question

Quizplus · Accepted Answer

This is a problem involving the future value of an annuity. The formula for the future value of an annuity is FV = P * [(1 + r)^n - 1] / r, where P is the payment amount, r is the annual interest rate, and n is the number of payments. Here, P = $2,000, r = 10% or 0.10, and n = 5 (since deposits were made annually from 2016 through 2020). Plugging these values into the formula gives FV = $2,000 * [(1 + 0.10)^5 - 1] / 0.10 = $2,000 * [1.61051 - 1] / 0.10 = $2,000 * 6.1051 = $12,210.20. However, since the question asks for the amount in the fund on January 2, 2021, one year after the final deposit, we need to account for one more year of interest on the entire amount. Thus, the total amount in the fund on January 2, 2021, is $12,210.20 * 1.10 = $13,431.22, which rounds to $13,431, making option B the correct answer.

Jessie's Dry Cleaner Began Making $2,000 Equal, Annual Deposits in a Fund