Jim will retire in 22 years.He will invest $100 each month for 11 years and then let the accumulated value continue to grow for the next 11 years.How much will be available at retirement? Assume 8%,
Compounded monthly.Round to the nearest dollar.
A)$50,573
B)$45,546
C)$48,125
D)$50,621
E)$48,550

Question

Quizplus · Accepted Answer

First, we need to find the future value of the monthly contribution of $100 for 11 years. Using the formula for future value of an annuity, we get:

FV = PMT x [((1 + r)^n - 1) / r]
where PMT is the monthly payment, r is the monthly interest rate, and n is the number of months

FV = 100 x [((1 + 0.08/12)^(11*12) - 1) / (0.08/12)]
FV = $20,319.19

Next, we need to find the future value of this amount for the remaining 11 years. Using the formula for future value of a lump sum, we get:

FV = PV x (1 + r)^n
where PV is the present value, r is the monthly interest rate, and n is the number of months

FV = 20,319.19 x (1 + 0.08/12)^(11*12)
FV = $50,620.60

Rounding to the nearest dollar, the answer is D) $50,621.

Jim Will Retire in 22 Years