# You wish to buy a $26,500 car. The dealer offers you a 4-year loan with a 10 per cent APR. a)... ## Question: You wish to buy a$26,500 car. The dealer offers you a 4-year loan with a 10 per cent APR.

a) What are the monthly payments?

b) How would the payment differ if you paid interest only?

## Month Loan Payments:

Loans are often financed using monthly payments. Each payment is of equal amount, but the distribution of the payment between interest payment and principal repayment changes over time, with an increasing portion of payment going toward principal over time.

a) The monthly payment is \$672.11.

We can use the following formula to compute the monthly payment for a loan with principal {eq}P {/eq}, monthly interest rate {eq}r{/eq} and number of monthly payments {eq}T{/eq}:

• {eq}\displaystyle \frac{Pr}{1 - (1 + r)^{-T}} {/eq}

In this question, the amount borrowed is 26,500, the effective monthly rate is 10%/12, and there are 4 * 12 = 48 monthly payments. Applying the formula, the monthly payment is:

• {eq}\displaystyle \frac{26,500*10\%/12}{1 - (1 + 10\%/12)^{-48}} = 672.11 {/eq}

b) If you pay interest only, then the monthly payment is simply the principal times the monthly interest rate, i.e.,

• 26,500*(10%/12) = 220.83