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

a$)$ What are the monthly payments?

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

c$)$ what is the unpaidbalance on the loan on April $1,2024?$