Question

ames Sprater of Grand Junction, Colorado, has been shopping for a loan to buy a used car. He wants to borrow $18,000 for four or five years. James' credit union offers a declining-balance loan at 9.25 percent for 48 months, resulting in a monthly payment of $450.07. The credit union does not offer five-year auto loans for amounts less than $20,000, however. If James borrowed $18,000, this payment would strain his budget. A local bank offered current depositors a five-year loan at a 9.34 percent APR, with a monthly payment of $376.62. This credit would not be a declining-balance loan. Because James is not a depositor in the bank, he would also be charged a $25 credit check fee and a $50 application fee. James likes the lower payment but knows that the APR is the true cost of credit, so he decided to confirm the APRs for both loans before making his decision. Round your answers to two decimal places.

Answer 1

Answer:

James' credit union loan rate is 8.88% APR, the local bank loan rate is 9.34% APR.

Explanation:

Hi, since in both cases payments would be done in a monthly basis, we have to assume that the rate that we are looking for is APR (compounded monthly), and since there is no additional information in regards that 9.25% rate, we can assume that this is effective annually, so let´s convert this effective monthly rate into APR (compounded monthly)

First, we have to convert it into an effective monthly rate, that is:

$r(month)=((1+r(annual))^{\frac{1}{12} } -1)$

$r(month)=((1+0.0925)^{\frac{1}{12} } -1)=0.00739963$

Then we multiply by 12 and we get  0,088796 , which is 8.88% APR (compounded monthly)

This way James can compare both credits. The cheaper loan is from the credit union.