Question

10. A car dealership offers a loan with 3.9% interest for 36 months, and you plan to purchase a car for $19,500. You can afford a down payment of $2,500.(a) What will your monthly payment be? $(b) How much will you pay in total for the car? $(c) How much will you pay in interest over the life of the loan? $

Answer 1

The monthly payment formula is :

`M=P*(r(1+r)^n)/((1+r)^n-1)`

where M is the monthly payment

P is the Financed amount

r is the rate of interest monthly, annual rate divided by 12

n is the number of payments

From the problem,

The financed amount is the difference between the car's cost and the down payment.

P = $19,500 - $2,500

P = $17000

The monthly interest rate is :

r = 3.9%/12 or 0.039/12 = 0.00325

n = 36 months

The monthly payment will be :

`\begin{gathered} M=17000*(0.00325(1+0.00325)^(36))/((1+0.00325)^(36)-1) \\ M=501.15 \end{gathered}`

a. M = $501.15

b. The total payment for the car is monthly payment multiplied by the number of payment made together with the downpayment.

501.15 x 36 + 2500 = $20,541.4

c. The interest is the difference between the total payment made and the financed amount.

I = 501.15 x 36 - 17,000 = $1,041.4