Goofy borrows $$450,000$ at an annual effective interest rate of $6\mathrm{.}6\%.$ He makes quarterly level payments of $$18,000$ until his final payment. He agrees to decrease the loan term by one period by opting for a balloon payment on his last payment. a$)$Find the total length of the loan $($in quarters$)$ b$)$and the amount of the final payment.

the answer is a$)32$ and b$)22430\mathrm{.}79$