Answer
$\$ 6655.58$
Work Step by Step
Since, the price decreases by $ 15\%$ and $15\%=0.15$, then we will multiply $1-0.15=0.85$ to the present value or term to get the value of the equipment the following year.
We know that
$a_{1}=15,000$
$\\a_{2}=15,000(0.85)\\ a_{3}=15,000(0.85)^{2}$
and so on.
This shows a geometric sequence with
$a_{1}=15,000$,
$r=0.85$
Hence, the $n^{th}$ term of the geometric sequence is given by the formula
$a_n=a_1r^{n-1} =15000(0.85)^{n-1}$
We need to find $a_5$.
Using the formula above gives:
$a_{5}=15,000(0.85)^{5-1}=15000(0.85^4)\approx \$ 6655.58$
