Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits. If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment, how much must each deposit be in order to accumulate the $40,000?
A) $ 6,132
B) $ 6,683
C) $23,844
D) $ 9,434

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity:
FV = PMT × [(1+r)^n - 1]/r
where FV is the future value, PMT is the equal annual payment, r is the annual interest rate, and n is the number of periods (in this case, 5).

Substituting the given values, we get:
40,000 = PMT × [(1+0.09)^5 - 1]/0.09
Solving this equation, we get:
PMT = 6,683.11

Therefore, each deposit must be $6,683.11 in order to accumulate $40,000 by the end of 5 years. The correct answer is B.

Xiao Xin Is Planning to Accumulate $40,000 by the End