John wants to buy a property for $$121,250$ and wants an $80$ percent loan for $$97,000.$ A lender indicates that a fully amortizing loan can be obtained for $30$ years $(360$ months$)$ at $9$ percent interest; however, a loan fee of $$4,800$ will also be necessary for John to obtain the loan.

Required:

a$.$ How much will the lender actually disburse?

b$.$ What is the APR for the borrower, assuming that the mortgage is paid off after $30$ years $($full term$)?$

c$.$ If John pays off the loan after five years, what is the effective interest rate?

d$.$ Assume the lender also imposes a prepayment penalty of $2$ percent of the outstanding loan balance if the loan is repaid within eight years of closing. If John repays the loan after five years with the prepayment penalty, what is the effective interest rate?