$4.$ You have decided to purchase an industrial property for $$40,000,000.$ A lender offers you $70$ percent LTV loan for $20$ years at $8\mathrm{.}25$ percent interest; however, $1\mathrm{.}5$ discount points will also be necessary for you to obtain this loan.

a$.$ What is the effective interest cost to the borrower, assuming that the mortgage is paid off after $20$ years $($full term$)?$

b$.$ Assume the lender also imposes a prepayment penalty of $2\mathrm{.}5$ percent of the outstanding loan balance if the loan is repaid within eight years of closing. If you repay the loan after five years with the prepayment penalty, what is the effective interest cost?