Question

In the year 1985, a house was valued at $119,000. 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

Let us take the annual growth rate as i.

If the year 1985 is considered as at t=0, the year 2005 is t=20 and year 2010 is t=25

By using the exponential function for the value at 2005, we have

a(1+i)^20 = y

where a = 110,000 (prinicple amount) and y = 145,000 (final amount)

substituting,

110000(i+1)^20 = 145000

(i+1)^20 = 1.3181818

.i+1= 1.0139; i = 0.0139 = 1.39%

The annual growth rate between 1985 and 2005 is 1.39 %

Considering the same growth, the amount in 2010 will be

y= 110000(1.0139)^25 = 155335 dollar