Question

You buy your first home after graduating college in the year 2020, the price is $210,000. With a 5% down payment, the bank offers you a 30 year mortgage at a rate of 4.125% APR.

1. How much is your monthly payment?

2. If you sell the house after 10 years, how much do you still owe on the mortgage and how much equity do you have in the home?

3. If typical home prices have been rising at 3% during those ten years and the house has been maintained and has not depreciated, after ten years how much do you sell the house for?

4. After giving the outstanding mortgage balance to the bank, how much is left for yourself?

5. Out of the money left after repaying the mortgage, how much is principal paid and how much is appreciation?

6. If inflation has been 2% during this time, calculate the 2020 purchasing power equivalent to the 2030 dollars from the home sale price.

7. How much did the home appreciate in real terms?

8. The federal government charges capital gains taxes of 15% on the difference between the purchase price and the sale price of an asset. How much do you have to remit to the Federal Government for the sale of the home?

9. What is your effective capital gains tax rate for this transaction when you consider inflation and only include real appreciation and not nominal appreciation?

10. Do you find the amount of capital gains tax you have to pay to be fair given the appreciation in real terms vs nominal terms and the rate of inflation over the ten years? Defend your answer.

Answer 1

1.

=PMT(4.125%/12,12*30,-210000*(1-5%))=$966.88

2.

Outstanding:

FV(4.125%/12,12*10,PMT(4.125%/12,12*30,-210000*(1-5%)),-210000*(1-5%))=$157,834.87

Equity=210000-157834.87=$52,165.13

3.

=FV(3%,10,0,-210000)=$282,222.44

4.

=282222.44-157834.87=$124,387.57

P.S.: I am not allowed to answer more than 4 questions