Chapter 11.3, Problem 12P

To determine

To calculate:

A purchase value of a house after two years from now

Answer to Problem 12P

A purchase value of a house after two years from now is $\$138,240$ .

Explanation of Solution

Given information:

Calculation:

A price increased one year by $20\%$ .

  $96000-80000=16000$

Then,

  $\frac{1600}{80000}=0.20$

Suppose $x$ is the starting price then the new price is

  $p=\left(x+0.2x\right)=1.2x$

The after one year price would be

  $1.2p=1.2\left(1.2x\right)$

Then year after that would be

  $1.2\left(1.2p\right)=1.2\left(1.2\left(1.2x\right)\right)$

If $n$ is the number of the years, then price after n years is given by equation.

The starting price: $x=80000$

Put the value of $t=3$

  $\begin{array}{l}p=x{\left(1.2\right)}^n\\ p=80000{\left(1.2\right)}^3\\ p=138240\end{array}$

A purchase value of a house after two years from now is $\$138,240$ .