Georgia deposits $4,000 every three months for five years. The first deposit is made on March 31, 2016, and the last deposit is made on December 31, 2020. The fund earns 16% and interest is compounded quarterly. How much money will Georgia have on December 31, 2020, immediately after her last deposit? Factors for future value of an annuity of $1 are
A) $123,876
B) $119,112
C) $110,034
D) $107,508

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula, considering the quarterly deposits and the quarterly compounding interest rate. Given the annual interest rate is 16%, the quarterly interest rate is 16%/4 = 4% per quarter. Georgia makes a total of 20 deposits ($4,000 every three months for 5 years). The future value of an annuity formula is FV = P * [(1 + r)^n - 1] / r, where P is the payment amount, r is the interest rate per period, and n is the total number of payments. Using the given factors for the future value of an annuity, the correct calculation aligns with the choice that provides the future value closest to the scenario described, which is $119,112. This choice accounts for the compound interest on the quarterly deposits over the five-year period.

Georgia Deposits $4,000 Every Three Months for Five Years