SOLUTION: In San Francisco, the average cost of a single-family house was $255,600 in 1990 and $677,300 in 2004. (a) Determine the approximate average annual inflation rate in single-family

Question 1131681: In San Francisco, the average cost of a single-family house was $255,600 in 1990 and $677,300 in 2004.
(a) Determine the approximate average annual inflation rate in single-family houses over the 14-year period. (Round your final answer to two decimal places.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
255,600 in 1990
677,300 in 2004

formula used is f = p * (1 + r) ^ n

f is the future value
p is the present value
r is the interest rate per year.
n is the number of years.

interest rate per year is he annual inflation rate in this problem.

formula becomes:

677300 = 255600 * (1 + r) ^ 14

divide both sides of this equation by 255600 to get:

677300 / 255600 = (1 + r) ^ 14

take the 14th root of each side of this equation to get:

(677300 / 255600) ^ (1/14) = 1 + r

subtract 1 from both sides of this equation to get:

(677300 / 255600) ^ (1/14) - 1 = r

solve for r to get r = .0720869662

convert to percent by multiplying by 100 to get average annual inflation rate percent = 7.20869662 percent.

if they want the answer as inflation rate and not percent, then the answer is .07 rounded to 2 decimal places.

if they want the answer as inflation rate percent, then the answer is 7.21% rounded to 2 decimal places.

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