The bank tells you that you can get a lower interest rate if you are willing to pay "points" up front. ("Points" is a fee paid immediately to the bank and is expressed as percentage points of the loan amount.) You are told that if you are willing to pay a fee equal to 2 percentage points of the loan amount to the bank immediately, you can finance your mortgage at the lower interest rate of only 4.75%.

c. How much would you have to pay the bank immediately to get the lower interest rate?

d. If you agree to pay the points and finance your same loan amount at the annual interest rate of 4.75%, then what would be your monthly payment?

e. What is the amount you would save each month between the payment in part 'b' and the payment in part 'd'?

f. If you plan to live in the house for four years and then sell it, what is the present value of your monthly savings over these four years at an annual discount rate of 5.125%? Are you better off paying the points or not?