Question

The formula for depreciation is V=P(1-r)t where P is the beginning price of the asset, r is the annual rate of depreciation written as a decimal, t is the number of years, and V is the value after t years. Jada's car depreciates at 12% each year. She bought the car for $24,700. What is the value of her car after 5 years?

Answer 1

The value of the car after 5 years is $ 13,035 to the nearest dollar.

Explanation:

The formula for depreciation is

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

where
`P=24,700\:dollars` is the beginning price of the asset,

`r=12\%` is the annual rate of depreciation written as a decimal,

`r=0.12`

`t=5` is the number of years, and V is the value after t years.

Now substitute all these values into the formula to get,

`V=24,700(1-0.12)^5`

This simplifies to,

`V=24,700(0.88)^5`

`\Rightarrow V=24,700(0.5277319168)`

`\Rightarrow V=13,034.97834`

The value of the car after 5 years is $ 13,035 to the nearest dollar.