Question

Below is a question from a powerpoint with the answers given, but I don't know the steps to get to the answer.

Q: Suppose you had to choose between a 12% 30-year mortgage or an 11.5% mortgage with 2 discount points. Which should you choose? Assume you wish to borrow $100,000.

A:

(i) For the 12% mortgage:

N = 360 I = 1.0 PV = 100,000 FV = 0 PMT = $1,028.61

(ii) For the 11.5% mortgage with 2 discount points:

N = 360 I = 11.5/12 PV = 100,000 FV = 0 PMT = $990.29

My questions are...

For (i) why is I = 1.0 and not 12? And why is N = 360 but not 30 years?

For (ii) why do we have to divide 11.5 by 12? And where does the 2 discount points come in?

Answer 1

For (i) we need to calculate monthly mortgage payment and thus we will need to consider monthly interest rate and total monthly payments and thus I used is 1% (12%/12) and number of payments used is 360 (30*12). If we use I=12% and N=30 years then we would get annual payments which is not correct as mortgage payment are monthly. Also, since payment is monthly the amount of mortgage loan keeps decreasing and thus interest keeps decreasing.

For (ii) similarly interest rate considered is monthly interest rate to calculate monthly payment which is calculated as 11.5%/12 which gives monthly interest rate of 0.96%.

The 2 discount points is the upfront cost paid by borrower to earn discount of market interest rate. Borrower had paid 2 discount points that is $2,000 (100,000*2%) and thus has received interest rate at discount of 11.5%. The 2 discount point is not useful to calculate the monthly mortgage payment but is used later to compare the benefit of lower mortgage payment under two mortgage type.