Anne wants to accumulate $25,000 by December 31,2019.To accumulate that sum,she will make twelve equal quarterly deposits of $1,761.55 at the end of March,June,September,and December for the next three years,beginning on March 31,2016,into a fund that earns interest compounded quarterly.What annual rate of interest must the fund provide to yield the desired sum?
A)3%
B)7%
C)12%
D)14%

Question

Quizplus · Accepted Answer

Using the formula for the future value of an annuity, we can calculate the total amount that Anne will have at the end of three years:

FV = PMT * ((1 + r/n)^(nt) - 1) / (r/n)

Where:
PMT = $1,761.55
n = 4 (quarterly compounding)
t = 3 (three years)
FV = $25,000

Solving for r, we get:

r = n * ((FV / PMT + 1)^(1/(n*t)) - 1)

r = 4 * ((25,000 / 1,761.55 + 1)^(1/(4*3)) - 1) = 12%

Therefore, the fund must provide an annual rate of interest of 12% to yield the desired sum of $25,000.

Anne Wants to Accumulate $25,000 by December 31,2019