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.