Question

In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $145,000. 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

Answer:

The annual growth rate is of 1.39%.

The value of the house in 2010 was $155,355.5

Step-by-step explanation:

The value of a house after t years is given by the following equation:

$V(t) = V_{0}(1 + r)^{t}$

In which $V_{0}$ is the initial value and r is the annual growth rate.

In the year 1985, a house was valued at $110,000. By the year 2005, the value had appreciated to $145,000. What was the annual growth rate between 1985 and 2005?

We want to find r, when $V_{0} = 110$ and $V(20) = 145$.

I use V(20) since 2005 is 20 years after 1985.

So

$V(t) = V_{0}(1 + r)^{t}$

$145 = 110(1 + r)^{20}$

$(1 + r)^{20} = 1.3182$

Applying the 20th root to both sides.

$1 + r = 1.0139$

$r = 0.0139$

So the annual growth rate is of 1.39%.

What was the value of the house in the year 2010?

2010 is 25 years after 1985. So

$V(t) = 110(1.0139)^{t}$

$V(25) = 110(1.0139)^{25} = 155.3355$

The value of the house in 2010 was $155,355.5