Robert Smith purchased a used car for $14,000. To pay for his purchase, he borrowed $12,500 from a local bank at 12%. The loan requires that Robert repay the loan by making 36 monthly payments. How much will Robert have to pay each month to repay the loan

$415.18

Explanation:

The calculation of the present value of a cash flow or other income stream that produces $1 in income over so many periods of time.

DATA

Amount borrowed = $12,500

Annual interest rate = 12.00%

Monthly interest rate = 1.00%

Period = 36 months

Let monthly payment be x

12,500 = x/1.01 + x/1.01^2 + x/1.01^3  … + x/1.01^35 + x/1.01^36

12,500 = x * (1 - (1/1.01)^36) / 0.01

12,500 = x * 30.107505

x = 12,500/30.107505  

x = 415.18

The monthly payment is $415.18

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