A borrower agrees to purchase a $$1\mathrm{.}5$ million value property, with a $25\%$ down payment, and take on a mortgage from the bank. The mortgage will be paid over $20-$years $($fixed$-$rate mortgage$)$ with a $7\mathrm{.}75\%$ quoted interest rate.

a$.$ Setup the amortization schedule.

b$.$ If the Bank offers $2$ points in exchange$$for a $7\mathrm{.}5\%$ interest rate, should you buy the points?