Christopher Schmidt, a $27-$year$-$old living in Denver, Colorado, has been a high$-$school teacher for $5$ years. For the past four months, he's been thinking about buying a Subaru Outback, but he feels that he can't afford a brand$-$new one. Recently, however, his friend John Daniels has offered to sell Christopher his fully loaded Subaru Outback. John wants $$26,900$ for his Outback, which has been driven only $8,000$ miles and is in very good condition. Christopher is eager to buy the vehicle but has only $$9,200$ in his savings account at Mountain Bank. He expects to net $$8,000$ from the sale of his Chevrolet Malibu, but this will still leave him about $$9,700$ short. He has two alternatives for obtaining the money.

Borrow $$9,700$ from the First National Bank of Denver at a fixed rate of $5\mathrm{.}5$ percent per annum, simple interest. The loan would be repaid in equal monthly installments over a three$-$year $(36-$month$)$ period.

Obtain a $$9,700$ installment loan requiring $36$ monthly payments from the Denver Teacher's Credit Union at a $5\mathrm{.}5$ percent stated rate of interest. The add$-$on method would be used to calculate the finance charges on this loan.

Using a financial calculator or a spreadsheet, determine the required monthly payments if the loan is taken out at First National Bank of Denver. Round the answer to the nearest cent.

$ $$ per month

a$.$ Compute the finance charges on the loan offered by First National Bank of Denver. Round the answer to the nearest cent.

$ $$

b$.$ Compute the APR on the loan offered by First National Bank of Denver. Round the answer to the nearest whole percentage.

$\%$

Determine the size of the monthly payment required on the loan from the Denver Teacher's Credit Union. Round the answer to the nearest cent.

$ $$ per month

a$.$ Compute the finance charges on the loan offered by the Denver Teacher's Credit Union. Round the answer to the nearest cent.

$$$

b$.$ Compute the APR on the loan offered by the Denver Teacher's Credit Union. Round the answer to the nearest whole percentage.