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Question

Barry Wood wants to buy a used car that costs $6000. He has two possible loans in mind. One loan is through the car dealer; it is a three-year add-on interest loan at 7% and requires a down payment of $300. The second is through his credit union; it is a three-year simple interest amortized loan at 8.5% and requires a 10% down payment.

(a) Find the monthly payment for each loan. (Give your answer to the nearest cent.)

(b) Find the total interest paid for each loan. (Give your answer to the nearest cent.)

Answer 1

1.For the car dealer loan,

With down payment of $300, effective loan (P) is 6000-300 = $5700

Also period (n) = 3 yrs = 36 months and rate (r) = 7%

Monthly interest = r/12* P = 7%/12 * 5700 = 33.25

Monthly principal = 5700/36 = 158.33

a. Monthly payment = 33.25 + 158.33 = $191.58

b. Total interest paid = 33.25*36 = $1197

2.For the credit union loan,

With down payment of 10% ($600), effective loan (P) is 6000-600 = $5400

Also period (n) = 3 yrs = 36 months, rate (r) = 8.5% and monthly rate (R) = 8.5/12 = 0.7083%

a. Monthly payment = P / [(1/R)*(1-1/(1+R)^n)] = 5400/[(1/0.007083)*(1-1/(1+0.007083)^36)] = $170.46

b. Total interest paid = 170.46 * 36 - 5400 = $736.6