Chapter 8, Problem 65RE

(a)

To determine

To calculate:

The value of fleet $t$ full year after it’s purchasing in terms of $n^{th}$ term of geometric progression.

Answer to Problem 65RE

The value of fleet $t$ full year after it’s purchasing in terms of $n^{th}$ term of geometric progression is $a_t=130,000{\left(0.7\right)}^t$ .

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_1=\$130,000\\ r=70\%\end{array}$

Formula used:

The geometric progression in terms of $n^{th}$ term is:

  $a_n=a_1{\left(r\right)}^{n-1}$ .

Calculation:

Consider, the company buys fleets for the six vans for $\$130,000$ and for the beginning year the depreciation value is $70\%$ .

Now, the geometric progression in terms of $n^{th}$ term is derived for the value of fleet $t$ full year after it’s purchasing as:

  $\begin{array}{l}{a}_n=a_1{\left(r\right)}^{n-1}\\ a_t=130,000{\left(70\%\right)}^t\\ a_t=130,000{\left(0.7\right)}^t\end{array}$