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

This is a amortized payment schedule.

Principal - a - $233,000

Time - 20 year

Interest rate - 5%

Periods in a year - 12

Total periods - n - 12*20 = 240

Interest rate per period - r - 5%/12 = 0.42%

a) Formula for calculating monthly payment = a/{[(1+r)^n]-1}/[r(1+r)^n]

Monthly payments = 233000/ ( (1.0042^240)-1)/(0.0042(1.0042)^240)

= 1542.85

b)

Interest of first payment = 0.42% of 233,000 = 970.833$

Thus, the amount that goes towards principal re payment = 1542.85-970.833 = 572.017$

c)

To find this out, lets create the schedule on excel:

To form the table:

Amount to be paid each period - determined through part a)

Interest payment - 0.42% of previous principal balance

Pricipal repayment - Amount to be paid - Interest

Balance - Previous balance - Principal repayment

As we can see: 811.793$ goes towards interest and 731.057$ towards principal repayment.

d) Present value of remaining principal:

From the previous part we know balance - 194099

Periods completed - 60 months or 5 years

PV = 194099/(1+5/100)^5

= 194099/1.05^5

=152082$

e) At zero interest rate the present value of payment remaining is equal to the value of payment remaing.

Thus, value = 194099$