Question

A car dealer will sell you a used car for $6,498 with $798 down and payments of $162.51 per month for 48 months. what is the interest rate and the APR?

Answer 1

Interest rate is 1.4% and APR is 16.8%.

Explanation:

Given,

The original cost of the car = $ 6,498,

Down payment = $ 798,

So, the present value of loan, P.V. = original cost - down payment

= $ 6,498 - $ 798 = $ 5700,

Now, the monthly payment, P = $ 162.51,

Number of months, n = 48,

Let r be the monthly interest rate,

Since, monthly payment formula of a loan,

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

`162.51=(5700r)/(1-(1+r)^(-48))`

By graphing calculator,

`r=0.014= 1.4\%`

Hence, interest rate = 1.4%,

And, APR = 12 × 1.4% = 16.8%.