Question

TED BORROWED $1,200 FOR TWO YEARS AND HE MADE MONTHLY PAYMENTS. IF THE TOTAL FINANCE CHARGE IS $175.92 WHAT IS THE APR? ANNUAL PERCENT RATE?

Answer 1

Given:

The borrowed amount is $1200.

The finance charge is $175.92

The period of time =2 years ( 24 months)

Required:

We need to find APR.

Explanation:

Let r be the APR.

The monthly interest rate is r/12.

$Total\text{ amount =1200+175.92=1375.92}$

P=1200 and t =24.

$Total\text{ amount =P\lparen1+}\frac{r}{n}\text{\rparen}^{nt}$$1375.92=1200(1+\frac{r}{12})^{12\times2}$$1375.92=1200(1+\frac{r}{12})^{24}$$\frac{1375.92}{1200}=\frac{1200}{1200}(1+\frac{r}{12})^{24}$$1.1466=(1+\frac{r}{12})^{24}$$1.00571631955=1+\frac{r}{12}$$1.00571631955-1=\frac{r}{12}$$0.00571631955\times12=r$$0.06859583463=r$

Multiply by 100, to find APR

$6.86\text{ \%}=APR$

Final answer:

$APR=6.82\text{ \%}$