Buying your own home is often mentioned as "the best investment you can make." In 1964,the average home sale price was $19,600.By 2009,the average home sale price had risen to $272,900.What was the average annual rate of change in the price of houses over this 45 year time period?
A)3.74% per year
B)6.03% per year
C)10.52% per year
D)12.16% per year

Question

Quizplus · Accepted Answer

To find the average annual rate of change, we can use the formula for compound interest: 
A = P(1 + r/n)^(nt) 
where A is the ending value, P is the beginning value, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. 
Using the values given, we get: 
272,900 = 19,600(1 + r/1)^(1 * 45)
Dividing both sides by 19,600 gives: 
13.93 = (1 + r)^45 
Taking the 45th root of both sides gives: 
1 + r = 1.0603 
Subtracting 1 from both sides gives: 
r = 0.0603 = 6.03% 
Therefore, the average annual rate of change in the price of houses over this 45 year time period was 6.03% per year.

Buying Your Own Home Is Often Mentioned as "The Best