During your education, you have borrowed $$30,000$ in student loans. You plan to make monthly payments to repay the debt. The interest rate is fixed at $7\mathrm{.}2\%$ APR.

a$.$ If the loans are for $10$ years, find the monthly payment.

b$.$ How much will you still owe after the $46$th payment?

c$.$ What is the effective rate? If you were the bank and advertising the loan, would you report the effective rate or APR? Explain.

d$.$ Suppose you decide to pay $$800$ per month instead of the required monthly payment. How long will it take you to pay off the loan?