show steps to calculation to put in excel!!! $-$Consider a $$5,000,000,8\mathrm{.}5\%$ APR, $30-$year mortgage with monthly payments, and expected realistic prepayment horizon of $7$ years. What is the contractual yield $($effective interest rate$)$ at issuance over the expected life of the loan under the following circumstances:

$($a$)$ No points or penalties

$($b$)$ One point of discount

$($c$)$ Three points of discount

$($d$)$ Three points of discount plus one point of prepayment penalty.