You get a 180-day $3,000 consumer loan at 9% interest You are required to pay a $100 setup fee at the time you get the loan. Based on a 365-day year, calculate the APR. Express the rate to the nearest tenth of a percent.

annual rate (APR) is  16.30%

Step-by-step explanation

Principal (P) for APR purposes is the amount of money you have use of= $3,000 - $100 fee 

                                                                                                                           = $2,900

Interest (I) for APR purposes is total finance charges: 

The interest on the loan is = P x R x T

                                              =$3,000 x 9%/100 x  180/ 365        

                                              =$3,000 x 0.09 x 0.49315

                                              =$270 x 0.49315                                     

                                              =$133.15

Total Finance charge = Interest on loan + set-up fees

                                     =$133.15 + $100

                                     =$233.15 

R= I / P x T

   =$233.15 / $2,900 x 180 / 365

   =$233.15 / $1,430.14

   =0.1630

         or

  =0.1630 x 100

   =16.30%

You are really paying an annual rate (APR) of 16.30%, considerably higher than the 9% stated rate. Because the loan is a consumer loan, the lender must inform you in writing what the APR is before you sign the loan agreement.