I need help finding the growth rate..

Question

In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $148,000. What was the annual growth rate between 1985 and 2005? Assume that the value continued to grow by the same percentage. What was the value of the house in the year 2010?



Answer 1

We can use the growth formula to figure this out. Recall that the growth formula is:

f(x) = a(1+r)^x

where a is the initial amount, r is the growth rate per time interval, and x is the number of time intervals. So we just need to plug in the values that we have and first find r:

148000 = 110000(1+r)²⁰

74/55 = (1+r)²⁰

(74/55)^1/20 = 1+r

r = (74/55)^1/20 - 1

r ≈ 0.0149472 or about 1.5%

Now we can plug this back into the formula to figure out the house value for 2010:

f(25) = 110000(1+0.0149472)²⁵

f(25) ≈ 159396.55

So the house value in 2010 is about $159,396.55.