Question

You purchased a property three years ago for $150,000. At the time, you put ten percent down and received a mortgage for ninety percent of the purchase price. Over the last three years, the value of the property has increased at an annual rate of three percent.a) Approximately how much is the property worth today? b) Ignore the increase in home equity over the last three years due to the amortization of the mortgage. What has been the overall increase in your equity in the property over the last three years?c) If your mortgage is a thirty-year fully amortizing fixed-rate mortgage at four percent interest, what is the total amount of equity in the home today, including the increase in its market value?d) What is the average annualpercentage increase in the value of equity the last three years?e) What important principle of investing is illustrated when comparing the average annual percentage increase in the value of this property relative to the annual percentage increase in the value of equity?

Answer 1

(a) Total Purchase Price = $ 150000, Property Growth Rate = 3 % and Tenure of Growth = 3 years

Therefore, Current Market Value of Property = 150000 x (1.03)^(3) = $ 163909.1

(b) Down Payment (Equity) = 10% of Total Purchase Price = 0.1 x 150000 = $ 15000 and Mortgage = 150000 - 15000 = $ 135000

Equity Value at Present = (163909.1 - 135000) = $ 28909.1

Increase in Equity Value = 28909.1 - 15000 = $ 13909.1

(c) Original Mortgage Tenure = 30 years. Mortgage Interest Rate = 4 %

Let the actual annual repayments be $ P

Therefore, 135000 = P x (1/0.04) x [1-{1/(1.04)^(30)}]

135000 = P x 17.29203

P = 135000 / 17.29203 = $ 7807.065

Mortgage Outstanding at Present (three years after mortgage was taken) = 7807.065 x (1/0.04) x [1-{1/(1.04)^(27)}] = $ 127486.1

Current Market Value of Home = $ 163909.1 and Mortgage Outstanding = 127486.1

Therefore, Current Equity Value = 163909.1 - 127486.1 = $ 36423

(d) Initial Equity Value = $ 15000 and Current Equity Value = $ 36423

Tenure = 3 years

Average Annual % Increase in Equity Value = [(36423/15000)^(1/3) - 1] = 0.344089 or 34.4089 % ~ 34.41 %

NOTE: Please raise a separate query for the solution to the last sub-part as one query is restricted to the solution of one complete question with upto a maximum of four sub-parts.