I take out a $$400,000$ loan, repaid in annual payments over the next $30$

years, at a fixed interest rate of $8\mathrm{.}5\%$

$($a$)$ What is my annual payment?

$($b$)$ Towards the end of the ${23}^{rd}$ payment, I inherit a large sum from an

estranged uncle and decide to pay off the balance of the loan. If I

pay off the loan right after the ${23}^{rd}$ payment, how much do I owe?