Chapter EP, Problem 8.8.1EP

To determine

To find:The value of the total amount combine in 3 years.

Answer to Problem 8.8.1EP

The desired amount is $\$96489.4$ .

Explanation of Solution

Given information:

The given information is

Amount = $\$175,000$

Rate= $r=18\%$

Time= $t=3$ .

Calculation:

An amount decreased by a certain percent over time is given by $y=a{\left(1-r\right)}^t$ .

Here, $a$ is the initial amount, $r$ is the rate of decrease, and $t$ is the time.

As per the data, Mr. R has the initial amount $\$175,000$ and the amount is depreciated at a rate of $18\%$ per year.

Here, $a=\$175,000,r=18\%=0.18,t=3$

Substitute all the value into $y=a{\left(1-r\right)}^t$

$\begin{array}{c}y=175000{\left(1-0.18\right)}^3\\ =175000{\left(0.82\right)}^3\\ =175000\times 0.551368\\ =\$96489.4\end{array}$

Therefore, the desired amount is $\$96489.4$ .