Question

Albert buys a car for $12,000. The value of the car depreciates about 9% per year. After about how many years will the car be worth $7500?

Answer 1

`5\ years`

Explanation:

we know that

The formula to calculate the depreciated value is equal to

`D=P(1-r)^(t)`

where

D is the depreciated value

P is the original value

r is the rate of depreciation in decimal

t is Number of Time Periods

in this problem we have

`P=\$12,000\\r=9\%=0.09\\D=\$7,500`

substitute in the formula above and solve for t

`\$7,500=\$12,000(1-0.09)^(t)`

`(7,500/12,000)=(0.91)^(t)`

Apply log both sides

`log(7,500/12,000)=t*log(0.91)`

`t=log(7,500/12,000)/log(0.91)=5\ years`