Fred deposits $50 at the end of every month for 5 years into a fund earning j₄ = 12%.What is the value of the fund one month after the final deposit?

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity to solve the problem:

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

where FV is the future value of the annuity, PMT is the monthly deposit, r is the monthly interest rate (12%/12 = 1%), and n is the number of months (5 years x 12 months/year = 60 months).

Plugging in the numbers, we get:

FV = 50 x [(1 + 0.01)^60 - 1] / 0.01 = $4,110.90

Therefore, the value of the fund one month after the final deposit is the future value plus the interest earned in that month, which is:

FV + (FV x 0.01) = $4,110.90 + $41.11 = $4,152.01

The closest answer choice is C ($4,110.90), which is the correct answer.

Fred Deposits $50 at the End of Every Month for 5