John wants to $$roll in$$ or finance the loan fee of $$5,200$ into the loan amount which would make the loan $$106,200$ and the interest rate is $5\%.$ Assume that the lender agrees to allow the loan fees to be included in the loan amount.

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?