The Smith family buys a home for a price of $$240,000.$ The loan they

take has an introductory rate of $2\mathrm{.}4\%$ compounded monthly for the first three years

and a rate of $4\mathrm{.}5\%$ compounded monthly after that. The total length of their loan is

$20$ years and end of month level payments are made.

a$)$ Find the monthly payment.

b$)$ Find the outstanding loan balance immediately after the $60$ th payment has been

made.

the answer is a$)1,434\mathrm{.}37$ and b$)187500\mathrm{.}99$