Question

At 1/1/2020, you take out a mortgage loan of $233,000. Your mortgage broker informs you that you can borrow the rest using a 20-year mortgage at an effective annual interest rate of 5%, with monthly compounding and constant monthly payments.

You may ignore all taxes and fees for the entirety of this problem. Note that today is t = 0 and after you buy the house you will make the first payment one month from now (t = 1).

1. a) Calculate the monthly payment on your home.

2. b) How much of your 1st payment goes toward paying down principal? How much goes toward

   paying interest?

3. c) How much of your 60th payment goes toward paying down principal? How much goes toward

   paying interest?

4. d) What is the present value of remaining principal balance after you make your 60th payment

   (at t = 60)?

Now, suppose you just make your 60th payment. There are still 180 payments remaining. Now, the Federal Reserve announces that the market interest rate is reset to 0%. However, you are still facing the same payment schedule.

e) At the new discount rate of 0%, what is the present value of your remaining payments?

Answer 1

a. Monthly Payment = $ 1537.70  

b. First payment will have $ 566.86 as principal and $ 970.83 as interest.

c. At the 60 payment $ 724.47 as principal and $ 813.23 as interest

d. Remaining Principal at the 60th payment = 194449.83.

Its present value = 1994449.83*(1+5%/12)^60 = $ 151516.36

e If discount rate = 0, then PV = 1994449.83*(1+0%/12)^60 = $  1994449.83

The calculation can be done using excel, the pic of which is shown below (Some rows are hidden to show the values at 60th payment)