Question

In the year 1985, a house was valued at $130,000. By the year 2005, the values had appreciated to $175,000.a. What was the annual growth rate between 1985 and 2005? Round to the nearest tenth of a percent.%b. Assume that the value continued to grow by the same percentage. What was the value of the house in the year2015? Round to the nearest thousand dollar.

Answer 1

We want to know the gowth rate of a house price between 1985 and 2005.

The value of the house at 1985 was $130,000 and at 2005 was $175,000, so the annual growth is:

$\begin{gathered} 175,000=130,000(1+x)^{(2005-1985)},\text{ x is the annual rate} \\ \frac{175000}{130000}=(1+x)^{20} \\ \frac{175}{130}=(1+x)^{20}\Rightarrow\sqrt[20]{\frac{175}{130}}=1+x \\ \\ x=\sqrt[20]{\frac{175}{130}}-1=1.015 \end{gathered}$

The annual growth rate is 1.5%.

For question b, if the grow continue to same percentage the value in 2015 is:

$\begin{gathered} \text{Price}_{2015}=175000\cdot(1+0.015)^{(2015-2005)} \\ \text{Price}_{2005}=175000\cdot1.015^{10}=203095 \end{gathered}$

The price of the house at 2015 is approx $203095