Question

18 months ago, you moved to Maine to run whitewater expeditions on the Penobscot River. You borrowed $20,000 to buy a trailer to transport the whitewater rafts. You have decided to repay the loan today. If the loan was a 4 year loan with monthly payments of $483.58 what is the amount that you owe the bank today? Assume that you have not missed any of your regular monthly payments.

Answer 1

Calculation of monthly interest rate:

Amount borrowed = $20,000
Monthly payment = $483.58
Time period = 4 years or 48 months

Let monthly interest rate be i%

$20,000 = $483.58 * PVIFA(i%, 48)

Using financial calculator:
N = 48
PV = -20000
PMT = 483.58
FV = 0

I = 0.625%

Monthly interest rate = 0.625%

Calculation of loan outstanding:

Period outstanding = 30 months

Loan outstanding = $483.58/1.00625 + $483.58/1.00625^2 + … + $483.58/1.00625^29 + $483.58/1.00625^30
Loan outstanding = $483.58 * (1 - (1/1.00625)^30) / 0.00625
Loan outstanding = $483.58 * 27.277919
Loan outstanding = $13,191.06