Question

A business purchases a theatre system for $2,500. If the value of the system decreases at a
rate of 13% per year, how much is the system worth after 2 years?
Please show how to do it, because I need to know how to do it again

Answer 1

Answer:

the system will be worth $1892.25 after 2 years.

Explanation:

as the value decreases: $\sf A = P(1 - \frac{r}{n})^{nt}$ ......notice the ' - '  as its *decreases*

given:

• P = 2500
• n = 1 per year
• t = 2 years
• r = 13%

solve:

$\sf A = 2500(1 - \frac{0.13}{1})^{1*2}$

$\sf A = 1892.25$

another way of doing it easily is:

[ $2500 * (100- 13)% ] * (100- 13)% = $1892.25

Answer 2

• P=2500
• r=13
• t=2

Use compound interest formula

$\\ \rm\hookrightarrow P(1-r/100)^t$

$\\ \rm\hookrightarrow 2500(1+0.13)^2$

$\\ \rm\hookrightarrow 2500(0.87)^2$

$\\ \rm\hookrightarrow 2500(0.76)$

$\\ \rm\hookrightarrow 1900$