f$)$ Problem $2$: Fixed rate mortgage

You take out a $15$ year fixed rate mortgage for $$500,000,$ and buy down the interest rate by

purchasing two points. After the points, the interest rate you agree to is $3\mathrm{.}25\%$ per annum. You

subsequently retain this mortgage for $3$ years, before prepaying it$.$

a$)$ What is the monthly payment on this mortgage? How much of the initial payment is interest,

and how much is principal?

b$)$ Over the three years, what is the total of all the interest payments you make on this loan?

What is the total value of the principal payments?

c$)$ Given that you paid off the loan after three years, would you have been better off $($in terms

of the effective interest rate$)$ if you hadn$$t paid points but taken a $3\mathrm{.}75\%$ interest rate? How

would this answer change if you had held the loan until maturity instead?

e$)$ What types of borrowers would generally not want to buy points on a fixed rate mortgage?

f$)$ Are prepayment penalties common for this type of loan? Explain.