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.

How much is your monthly payment

+ PMT = 966.88

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

+ Owe Mortgage = 157,835.48

+ Equity on Home = 52,164.52

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

+ House after ten years sells = 282,222.44

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

+Left = 124,386.52

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

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

How much did the home appreciate in real terms?

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?

Answer 1

How much did the home appreciate in real terms?

A. - Home sale price in 2030 = $282,222.14

Inflation rate = 2% per annum.

B - Discounting 2030 house value to say present value(Yr 2020) = $231,520.69 [this is the discounted value of the sale price in 2030 to the value in 2020 discounted at the rate of inflation]

C. - Purchase price in Yr 2020 = $210,000.

Hence the difference between the discounted 2020 year value, of the house price is 2030 - the purchase price of house in 2020 is the home appreciation in real terms: B-C = Home appreciation in real terms.

(231,520.69 - 210,000) = $21,520.69 or 10.247% of appreciation in real terms.

How much do you have to remit to the Federal Government for the sale of the home?

Tax rate of 15% on capital gains: (difference between the purchase price and the sale price of an asset) * 15%

(A - C) * 15% = ($282,222.44 - $210,000) *15% = $10,833.366 is the amount to be remitted to the Federal Government for the sale of the home.