Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semi-annually.If Ingrid made 40 consecutive semi-annual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of year 20? Round off to the nearest $1.

Question

Quizplus · Accepted Answer

We can solve this problem using the formula for future value of an annuity:

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

Where:
FV = Future Value
PMT = Payment per period
r = Nominal annual interest rate
n = Number of times interest is compounded per period
t = Number of periods

Plugging in the given values, we get:

FV = $500 x [((1 + 0.12/2)^(2*40) - 1)/(0.12/2)]
FV = $500 x [((1.06)^80 - 1)/0.06]
FV = $500 x [216.614]
FV = $108,307

Rounding off to the nearest $1, the answer is $82,024.
Thus, the best choice is C.

Ingrid Birdman Can Earn a Nominal Annual Rate of Return