A car is purchased for $30,000. It depreciates at a rate of 18% per year. What equation would represent the value, y, of the car after x number of years? Use this equation to find the value of the car after five years.
The standard equation for depreciation is
FV=PV(1-i)n
where
FV=future value
PV=present value
i=depreciation rate per annum, in decimals
n=number of years
Example:
Find the value of a car after 10 years if it was purchased for 50000 and depreciated at 20% per year.
PV=50000
i=0.20
n=10
FV(after 10 years)
=PV(1-i)^n
=50000(1-0.20)^10
=$5368.71
To find the equation that represents the value of the car after x number of years, we can use the initial value of $30,000 and the depreciation rate of 18% per year.
Since the car depreciates at a rate of 18% each year, its value after one year would be 82% (100% - 18%) of its original value. Therefore, we can calculate the value of the car after x years using the formula:
y = 30000 * (1 - 0.18)^x
Simplifying,
y = 30000 * (0.82)^x
Now let's find the value of the car after five years:
Substituting x = 5 into the equation:
y = 30000 * (0.82)^5
Using a calculator, we can evaluate this expression:
y ≈ $15,521.58
Therefore, the value of the car after five years would be approximately $15,521.58.