Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent.
A)$244.24 per month
B) $220.71 per month
C) $281.72 per month
D) $286.72 per month
E) $186.89 per month

Question

Determine the monthly payment necessary to accumulate $30,000 in a fund paying 6% per year, compounded monthly, for 8 years. (Assume end-of-period deposits and compounding at the same intervals as deposits.) Round your answer to the nearest cent. ​
A)$244.24 per month
B) $220.71 per month
C) $281.72 per month
D) $286.72 per month
E) $186.89 per month

Quizplus · Accepted Answer

The correct answer is A. $244.24 per month.The formula for the future value of an annuity is:FV = PMT * (((1 + r/n)^(n*t)) - 1) / (r/n))where:PMT is the monthly paymentFV is the future valuer is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:FV = $30,000r = 6% = 0.06n = 12 (monthly compounding)t = 8Plugging these values into the formula, we get:$30,000 = PMT * (((1 + 0.06/12)^(12*8)) - 1) / (0.06/12))Solving for PMT, we get:PMT = $244.24

Determine the Monthly Payment Necessary to Accumulate $30,000 in a Fund