Question 1153440: In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated exponentially to $150,000. What was the annual growth rate between 1985 and 2005? (Round your answer to two decimal places.)
%
Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010? (Round your answer to the nearest dollar.)
$
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! house was 110,000 in 1985.
house is 150,000 in 2005.
2005 - 1985 = 20 years.
formula to use is f = p * (1 + r) ^ n
f is the future value.
p is the present value
r is the interest rate per time period (years in this case).
n is the number of time periods (years in this case).
formula becomes:
150,000 = 110,000 * ( 1 + r) ^ 20
divide both sides of this equation by 110,000 to get:
150,000 / 110,000 = (1 + r) ^ 20
take the 20th root of both sides of the equation to get:
(150,000 / 110,000) ^ (1/20) = 1 + r
subtract 1 from both sides of the equation to get:
(150,000 / 110,000) ^ (1/20) - 1 = r
solve for r to get:
r = .0156286155.
the annual growth rate is .0156286155
confirm by taking 110,000 and multiplying it by (1 + .0156286155) ^ 20.
you will get 150,000.
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