James Sprater of Grand Junction, Colorado, has been shopping for a loan to buy a used car. He wants to borrow $$18,000$ for four or five years. James' credit union offers a declining$-$balance loan at $9\mathrm{.}15$ percent for $48$ months, resulting in a monthly payment of $$449\mathrm{.}21.$ 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 $9\mathrm{.}34$ percent APR, with a monthly payment of $$376\mathrm{.}62.$ This credit would not be a declining$-$balance loan. Because James is not a depositor in the bank, he would also be charged a $$25$ credit check fee and a $$60$ 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.

What is the APR for the credit union loan?

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Use the n$-$ratio formula to calculate and confirm the APR on the bank loan as quoted for depositors.

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What is the add$-$on interest rate for the bank loan?

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What would be the true APR on the bank loan if James did not open an account to avoid the credit check and application fees?

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