Houses in an area have been appreciating at the rate of 4 percent a year. An inv

Question

Houses in an area have been appreciating at the rate of 4 percent a year. An investor expects to finance a home purchase with a loan-to-value ratio of 80 percent. a) What is the expected appreciation rate on home equity (EAHE) for the first year? b) What if the expected rate of appreciation in the house price for the second year (year 2) is 2% and for year 3 is 5%. What is the average rate of appreciation in home equity over the 3-year period? Calculate both an arithmetic and geometric average. Show your work. Review problem 2 at end of chapter 7.

Explanation / Answer

Answer :

1.For the first year appreciation rate as given would be 4 %.( given in the question )

Assuming , The loan to value ratio does not play any role here.

2.Arthematic Average = (4+2+5)/3 ( Rate for 1st year + rate for 2nd year + rate for third year )/ No.of years

Therefore, Arthimatic average rate of appreciation = 3.67 %

3. Geometric Average = [(1 +rate 1) * (1+ rate 2) * (1+ rate 3) ] raised to 1/n , where n = no . of total years

Hence Geometric Average = [(1+0.04)* ( 1+0.02) * ( 1+0.05)] raised to 1/3

hence , geometric average rate of appreciation = 1.03

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