After visiting several automobile dealerships, Richard selects the used car he wants. He likes its $10,000 price, but financing through the dealer is no bargain. He has $2,000 cash for a down payment, so he needs an $8,000 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 $8,000 for a period of four years at an add-on interest rate of 11 percent. What is the total interest on Richard’s loan? What is the total cost of the car? What is the monthly payment? What is the annual percentage rate (APR)?

A. $3,520

B. $13,520

C. $240 monthly

D. 21.55%

Explanation:

A. Calculation for the total interest

Using this formula

Interest = (Principal) (Rate) (Time)

Let plug in the formula

Interest = (8000)(.11)(4)

Interest = $3,520

B. Calculation for the total cost of the car

Using this formula

Total Cost = Down Payment + Principal amount Borrowed + Interest amount

Let plug in the formula

Total Cost = $2,000 + $8,000 + $3,520

Total Cost = $13,520

C. Calculation for the monthly payment

Using this formula

Monthly Payment = (Principal amount Borrowed + Total interest amount ) / Total number of payments

Monthly Payment = ($8,000 + $3,520) / 48

Monthly Payment=$11,520/48

Monthly Payment=$240 monthly

Note 4-year * 12 months will give us 48months

D. Calculation for the annual percentage rate (APR) using this formula

APR= (2 × n × I) / [P × (N + 1)]

Let plug in the formula

APR = (2 × 12 × $3,520) / [$8,000 × (48+1)]

APR =$84,480/$8,000×49

APR=$84,480/$392,000

APR=0.2155×100

APR= 21.55%

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