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

• 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`

Answer 2

the system will be worth $1892.25 after 2 years.

Step-by-step explanation:

as the value decreases:
`\sf A = P(1 - (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 - (0.13)/(1))^(1*2)`

`\sf A = 1892.25`

another way of doing it easily is:

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