Chapter 9.7, Problem 13PPS

(a)

To determine

An equation for the median house price for t years after 2004

Answer to Problem 13PPS

The equation for the median house price for t years after 2004 $A=221000{\left(1.0086\right)}^t$

Explanation of Solution

Given information:

The median house price in the United State increased an average of 8.6% each year between 2002 and 2004

  

So the value is

  $\begin{array}{c}P=221000\\ t=t\\ r=8.6\%\\ =\frac{8.6}{100}\\ =0.086\\ n=1\end{array}$

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
  $\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find the equation number of memberships sold at work-out-gym t years after 2001 is as below:

  $\begin{array}{c}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =221000{\left(1+\frac{0.086}{1}\right)}^{1t}\\ A=221000{\left(1.0086\right)}^t\end{array}$

Thus, the equation for the median house price for t years after 2004 $A=221000{\left(1.0086\right)}^t$

(b)

To determine

The median house price in 2015

Answer to Problem 13PPS

The median house price in 2015 is $\$242658$

Explanation of Solution

Given information:

The median house price in the United State increased an average of 8.6% each year between 2002 and 2004

So the value is

  $\begin{array}{l}A=221000{\left(1.0086\right)}^t\\ t=11\end{array}$

Concept used:

• The formula for compound interest: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$
• Where
$\begin{array}{l}A=\text{final}\text{amount}\\ P=\text{principal}\text{balance}\\ r=\text{rate}\text{of}\text{interest}\\ n=\text{number}\text{of}\text{times}\text{intrest}\text{applied}\text{per}\text{time}\text{period}\\ t=\text{number}\text{of}\text{time}\text{periods}\end{array}$

Calculation:

To find the median house price in 2015 is as below:

  $\begin{array}{c}A=221000{\left(1.0086\right)}^t\\ A=221000{\left(1.0086\right)}^{11}\\ =221000\times 1.098\\ A=242658\end{array}$

Thus, the median house price in 2015 is $\$242658$