Question

Jack Fitzgerald wishes to purchase a used car that has a cash price of ​$11 comma 000. The installment terms include a down payment of ​$4 comma 000 and 36 monthly payments of ​$225. ​a) What finance charge will Jack​ pay? ​b) What is the APR to the nearest half​ percent?

Answer 1

a) Finance chare = $1,100.

b) APR = 9.75%.

Step-by-step explanation:

a)

Amount needs to be finance = 11,000 - 4,000 = $7,000.

Amount repayment = 225 x 36 = $8,100.

=> Finance charge = Amount repayment - Amount needs to be finance = $1,100.

b)

We apply the PV for annuity formula to find the interest rate per one month denoted as i:

Amount needs to be finance = (equal monthly installment x i) / [ 1 - (1+i)^-36 ]

or 7,000 = (225/i) x [1 - (1+i)^-36 ] <=> i = 0.811%.

APR = 12 x i = 9.732% .