Marks

$5.$ Suppose you borrowed $$40,000$ for a car loan on January $1,2024$ with an annual interest rate of $7\%$ per year. The balance on the loan is amortized over $8$ years with equal monthly payments at the end of each month. $($This means the unpaid balance on January $1,2032$ should be $$0).$

$($a$)$ What are the monthly payments?

$($b$)$ How much interest was paid during the $8$ years of the loan?

$($c$)$ What is the unpaid balance on the loan on April $1,2024?$