Chapter 12.3, Problem 84AYU

To determine

To find: The value of equipment after fifth year.

Answer to Problem 84AYU

The value of equipment after fifth year is $\$6,655.579688$ .

Explanation of Solution

Given information:

The given new cost of equipment is $15,000 and depreciated the value by $15\%$ .

Calculation:

Calculate the value of equipment. For the value after $1$ year.

  $\begin{array}{l}=15000-\left(\frac{15}{100}\times 15000\right)\\ =15000\times \left(1-\frac{15}{100}\right)\\ =15000\times \left(\frac{85}{100}\right)\\ =15000\times \left(\frac{17}{20}\right)\end{array}$

For the value after $2$ year is,

  $\begin{array}{l}=15000\left(\frac{17}{20}\right)-\left(\frac{15}{100}\times \left(15000\times \frac{17}{20}\right)\right)\\ =15000\times \frac{17}{20}\left(1-\frac{15}{100}\right)\\ =15000\times \frac{17}{20}\left(\frac{85}{100}\right)\\ =15000\times \frac{17}{20}\times \frac{17}{20}\end{array}$

The common is ratio is $r=\frac{17}{20}$ .

The value of equipment after five years is,

  $\begin{array}{c}{a}_1=a_1{r}^{n-1}\\ a_6=15000{\left(\frac{17}{20}\right)}^{6-1}\\ =15000{\left(\frac{17}{20}\right)}^5\\ =6,655.579688\end{array}$

Therefore, the value of equipment after fifth year is $\$6,655.579688$ .