You are considering the purchase of a property today for 300

You are considering the purchase of a property today for $300,000. You plan to finance it with an 80 percent loan. The appreciation rate on the property value is expected to be 4 percent annually for the next three years.

Calculate the expected annual average rate of appreciation on home equity for the next 3 years, using both the “arithmetic” and the “geometric” average calculations. (Show and explain all necessary calculations.) What do the two mean?

What if you now think that a $300,000 purchase price may be somewhat high and that if you pay this price, the expected appreciation rates in your house price will be as follows: year 1=0%, year 2=2%, and year 3=3%. Recalculate both the “arithmetic” and the “geometric” averages. (Show and explain all necessary calculations.) What do the two mean?

Solution

Value of the property today = $300,000

Rate of appreciation = 4% per year for 3 years

therefore, value of the property after 1 year at 4% = $300,000 x 1.04 = $312,000

value of the property after 2 years at 4% = $312,000 x 1.04 = $324,480

Hence value of the property after 3 years at 4% = $324,480 x 1.04 = $337,459.2

Arithmetic annual average appreciation rate = (337,459.2 / 300000) = 1.124

1.124-1 = 0.124 x 100 = 12.4 for 3 years, and therefore annual average rate of appreciation = 4.133 %

Geometric:

(337,459.2 / 300000) = 1.124 For Geometric average we should raise the value by 1/n th ( n = no. of years)

i.e 1.124^(1/3) = 1.04 hence 1.04-1 = 0.04 and average annual rate of appreciation = 0.04 x 100 = 4%

For these kind of problems Geometric annual average rate is reality than Arithmetic

Following the above procedure and now considering the appreciation rates to be 1=0%, 2=2%, 3=3%

Value of property after 3 years = $315180

And , applying the above methods for arithmetic and geometric the annual average rate of appreciations are 1.68% and 1.658% respectively.