Question

Some lenders charge an up-front fee on a loan, which is subtracted from what the borrower receives. This is typically described as "points" (where on point equals 1% of the loan amount). The federal government requires that this be accounted for in the APR that discloses the loan's cost.

(1) A 5-year auto loan for $20,000 has monthly payments at an 8% nominal annual rate. If the borrower must pay a loan origination fee of 2.5 points, which is the true effective cost of the loan? What would the APR be?
(2) If the car is sold after 3 years and the loan is paid off, what is the effective interest rate and the APR?

Answer 1

(1) For the 5-year auto loan of $20,000 with monthly payments at an 8% nominal annual rate and a loan origination fee of 2.5 points:

Monthly payment amount: $405.53
Total amount paid over the entire loan term: $24,331.67
APR for the entire loan [ term: 4.83%
(2) If the car is sold after 3 years and the loan is paid off:

Remaining loan balance after 3 years: $8,966.44
Total amount paid over 3 years: $14,599.00
APR for the 3-year period: 6.78% ]