Answer:
The value of the car after 5 years is $ 13,035 to the nearest dollar.
Step-by-step explanation:
The formula for depreciation is
[tex]V=P(1-r)^t[/tex]
where [tex]P=24,700\:dollars[/tex] is the beginning price of the asset,
[tex]r=12\%[/tex] is the annual rate of depreciation written as a decimal,
[tex]r=0.12[/tex]
[tex]t=5[/tex] is the number of years, and V is the value after t years.
Now substitute all these values into the formula to get,
[tex]V=24,700(1-0.12)^5[/tex]
This simplifies to,
[tex]V=24,700(0.88)^5[/tex]
[tex]\Rightarrow V=24,700(0.5277319168)[/tex]
[tex]\Rightarrow V=13,034.97834[/tex]
The value of the car after 5 years is $ 13,035 to the nearest dollar.
