The city of Metropolis borrows $88,000,000 so that it can build a football stadium.It plans to set up a sinking fund that will repay the loan 10 years later.Assume a 6% interest rate per year.What will Metropolis have to place in the fund in the beginning of each year in order to pay back the$88,000,000?
A)$6,298,472
B)$6,676,380
C)$534,309
D)$536,980

Question

Quizplus · Accepted Answer

The correct answer is A.The formula for the annual payment into a sinking fund is:PMT = PV * (r / ((1 + r)^n - 1))where:PMT = annual paymentPV = present value of the loanr = annual interest raten = number of yearsIn this case, the present value of the loan is $88,000,000, the annual interest rate is 6%, and the number of years is 10. Plugging these values into the formula, we get:PMT = 88,000,000 * (0.06 / ((1 + 0.06)^10 - 1))PMT = 88,000,000 * (0.06 / ((1.06)^10 - 1))PMT = 88,000,000 * (0.06 / (1.790847697 - 1))PMT = 88,000,000 * (0.06 / 0.790847697)PMT = 88,000,000 * 0.075862378PMT = $6,298,472Therefore, Metropolis will have to place $6,298,472 in the fund at the beginning of each year in order to pay back the $88,000,000 loan.

The City of Metropolis Borrows $88,000,000 So That It Can