A loan for $$152,000$ has a nominal interest rate of $7\mathrm{.}5\%$ per year that is compounded quarterly and has a duration of $5$ years. Determine the following: a$.$ The effective annual percentage rate $($APR$).$ b$.$ Assume that equal payments are made each quarter for the duration of the loan $($includes interest and loan payback$).$ Determine the payment.