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After visiting several automobile dealerships, Richard selects the car he wants. He likes its $10,500 price, but financing through the dealer is no bargain. He has $2,100 cash for a down payment, so he needs an $8,400 loan. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $8,400 for a period of two years at an add-on interest rate of 10 percent.

a) What is the total interest on Richard’s loan?

b) What is the total cost of the car?

c) What is the monthly payment?

d) What is the annual percentage rate (APR)?

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Answer:

a) Total Interest Paid in 24 months is $1680

b) Total Cost of the car is $12180

c) Monthly Payment is $420

d) Annual Percentage Rate  is 10.47%

Explanation:

(a) Loan Amount = $8400

Interest Rate = 10%

Monthly Interest = 8400 x (10%/12)

                            = $70

Total Interest Paid in 24 months = 24 x 70

                                                     = $1680

(b) Total Cost of the car = Loan Amount + Interest Paid + Down payment

                                       = 8400 + 1680 + 2100

                                        = $12180

(c) Monthly Principal Payment = 8400/24

                                                  = $350

Monthly Payment = Monthly Interest Payment + Monthly Principal Payment

                              = 70 + 35

                              = $420

(d) Annual Percentage Rate = (1+ 0.10/12)12 - 1

                                              = 0.1047

                                               = 10.47%

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