Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 10%/year compounded monthly. If the future value of the annuity after 10 years is $70,000, what was the size of each payment? Round your answer to the nearest cent.
A) R = $379.20
B) R = $341.72
C) R = $284.37
D) R = $365.25

Question

Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 10%/year compounded monthly. If the future value of the annuity after 10 years is $70,000, what was the size of each payment? Round your answer to the nearest cent. ​
A) R = $379.20
B) R = $341.72
C) R = $284.37
D) R = $365.25

Quizplus · Accepted Answer

Using the formula for future value of an ordinary annuity:

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

where FV is the future value of the annuity, R is the size of each payment, r is the annual interest rate (10%), n is the number of compounding periods per year (12), and t is the number of years (10).

Plugging in the values, we get:

$70,000 = R(((1 + 0.1/12)^(12*10) - 1)/(0.1/12))

Solving for R, we get:

R = $341.72

Therefore, the best choice is B.

Suppose Payments Were Made at the End of Each Month