Question

In the year 1985, a house was valued at $120,000. By the year 2005, the value had appreciated exponentially to $145,000. 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 1

The annual growth rate between 1985 and 2005 is 0.95%

The value of the house in the year 2010 is $152,018

Explanation:

Let the annual growth rate = r

Value of the house in year 1985 = $120,000

Value of the house in year 2005 = $145,000

Time (t) = 2005 - 1985

= 20 years

A = P (1 + r)^t

145000 = 120000 (1 + r) ^20

(1 +r)^20 = 145000 / 120000

(1 +r)^20= 1.2083

(1 +r)^20= (1.2083)^1/20

(1 +r)^20= 1.0095

r = 1.0095 - 1

r = 0.0095

r% = 0.0095 x 100

= 0.95%

Value of the house in year 2010

=145000(1 + r)^5

=145000 (1 + 0.0095)^5

= 145000 x 1.0484

=$152,018