$28$ You are buying a new home for $$116000.$ You have an agreement with the savings and loan company to borrow the needed money if you pay $20$ percent in cash and monthly payments for $30$ years at an interest rate of $4\mathrm{.}15$ percent compounded monthly.

$($a$)$ What monthly payments will be required?

$($b$)$ How much principal reduction will occur in the first payment?