Problem
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 (Use IRR method).