Question

How long will it take to pay off a loan of ​$54,000 at an annual rate of 11 percent compounded monthly if you make monthly payments of ​$750​? Use five decimal places for the monthly percentage rate in your calculations.

Answer 1

Principal = $54,000

Interest rate = 11%

Monthly payment = $750

Monthly Payment = (interest rate / Compounding frequency) / 1 - (1 + interest rate / compounding frequency)^{- (no of periods * Compounding frequency)} * Principal

$750 = (11% / 12) / 1 - (1 + 11% / 12)^{- (no of periods * 12)} * $54,000

1 - (1 + 11% / 12)^{- (no of periods * 12)} = ($54000 / $750) * (11% / 12)

1 - (1 + 11% / 12)^{- (no of periods * 12)} = 0.66

(1 + 11% / 12)^{- (no of periods * 12)} = 0.34

Apply log to both sides

log((1 + 11% / 12)^{- (no of periods * 12)}) = log (0.34)

- (no of periods * 12) * log (1 + 11% / 12) = log (0.34)

- (no of periods * 12) = log (0.34) / log (1 + 11% / 12)

- (no of periods * 12) = -118.2269

No of months required to make payments = 118.23 months