Question

You just bought a rent house for $200,000, with $40,000 down and the balance in the form of a 15-year amortization mortgage at a fixed rate of 4.0% and monthly payments. Your principal, interest, property tax, and insurance, plus all costs of maintaining the property, are covered by your rent.

a) How much are your monthly mortgage payments?

b) The University grows, and prices appreciate at the rate of 6% per year. What will the value of the house be in 6 years? What will the outstanding principal of the debt be (assume no extra payments)? What will the value of the equity be?

c) Using CAGR, what is your rate of return on your equity? There was a wealth transfer from lender to borrower, over the first 6 years of the mortgage? Why? Generalize about how wealth transfers can occur between borrowers and lenders.

d) What will be the value of the house be in 15 years? How much will your equity be worth? How much will be your debt?

e) Describe the theories of the term structure of interest rates that explain a normal upward sloping, flat, and downward sloping yield curve. Which type of curve is often (but not always) followed by an economic downturn and stock market correction/crash?

Answer 1

House Price = $ 200000, Down Payment = $ 40000, Tenure = 15 years or 180 months, Interest Rate = 4 % per annum or 0.33 % per month,

Let the monthly repayments be $ K

Loan Amount = 200000 - 40000 = $ 160000

160000 = K x (1/0.0033) x [1-{1/(1.0033)^(180)}]

K = $ 1180.29

(b)

(i) Price Appreciation Rate = 6% per annum

Price after 6 years = 200000 x (1.06)^(6) = $ 283703.82

(ii) The outstanding principle will be equal to the sum of the present values of remaining monthly repayments at the end of Year 6.

Principle Outstanding = 1180.29 x (1/0.0033) x [1-{1/(1.0033)^(108)}] = $ 107083.25

(iii) Equity Value = House Price - Principle Outstanding = 283703.82 - 107083.25 = $ 176620.57

NOTE: Please raise separate queries for solutions to the remaining unrelated questions.