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

Answer:

Interest rate is 1.4% and APR is 16.8%.

Step-by-step 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,

$P=\frac{PV(r)}{1-(1+r)^{-n}}$

$162.51=\frac{5700r}{1-(1+r)^{-48}}$

By graphing calculator,

$r=0.014= 1.4\%$

Hence, interest rate = 1.4%,

And, APR = 12 × 1.4% = 16.8%.