This problem is a complex financial problem that requires several skills, perhaps some from previous sections.

Clark and Lana take a $30-$year home mortgage of $$125,000$ at $7\mathrm{.}2\%,$ compounded monthly. They make their regular monthly payments for $5$ years, then decide to pay $$1500$ per month.

$($a$)$ Find their regular monthly payment. $($Round your answer to the nearest cent.$)$

$

$($b$)$ Find the unpaid balance when they begin paying the $$1500.($Round your answer to the nearest cent.$)$

$

$($c$)$ How many payments of $$1500$ will it take to pay off the loan? Give the answer correct to two decimal places.

monthly payments

$($d$)$ Use your answer to part $($c$)$ to find how much interest they save by paying the loan this way. $($Round your answer to the nearest cent.$)$