Consider two ways of getting a mortgage on a house worth $750,000. You plan to

make a down payment of $300,000 at closing. You need to borrow the rest of the $450,000.

The first option is a 15 year fixed-rate mortgage at a 5.25% effective annual interest rate

(assume monthly compounding with 12 payments per year to get a monthly interest rate).

In the second option, you can “buy” a lower effective annual interest rate of 4.5% by paying

the bank an additional $25,000 cash at closing (also assume 12 monthly payments over the

year with monthly compounding). You are still borrowing $450,000, but now you are paying

an additional $25,000 in cash up front at origination (this is commonly called paying “points”

on a mortgage). All other costs are the same under both options.

- a) Using the monthly interest rate over 180 payments, what would your monthly

payment be under the first scenario?

- b) Using the monthly interest rate over 180 payments, what would be your

monthly payment under the second scenario?

- c) Show which option is better.