You buy a used car for $20,000. It depreciates at the rate of 21% per year. Find the value of the car for the given years (5 and 8)
I'm using the equation v=c(1-r), and i end up getting 6154.11 ; im not sure if i subtract that from 20,000 or if that is my answer
After n years,
v = c(1-r)^n = 20000 * 0.79^n
no need to subtract from anything, unless you want to see how much its value has declined.
6154.11 is the value after 5 years.
To find the value of the car after a certain number of years, you can use the formula you mentioned:
v = c(1 - r)
Where:
v = value of the car after depreciation
c = initial cost of the car
r = depreciation rate per year
Given that the initial cost of the car is $20,000 and the depreciation rate is 21%, let's calculate the value of the car after 5 and 8 years.
For 5 years:
v = $20,000(1 - 0.21) = $20,000(0.79) = $15,800
For 8 years:
v = $20,000(1 - 0.21) = $20,000(0.79) = $15,800
So the value of the car after 5 years is $15,800 and the value of the car after 8 years is also $15,800.
To find the value of the car for a given number of years, you can use the formula:
v = c(1 - r)^t
Where:
v = value of the car after t years
c = initial cost of the car
r = depreciation rate per year (in decimal form)
t = number of years
In this case, you have:
c = $20,000 (initial cost of the car)
r = 21% or 0.21 (depreciation rate per year as a decimal)
To find the value of the car after 5 years, you would substitute these values into the formula:
v = $20,000(1 - 0.21)^5
v ≈ $20,000(0.79)^5
v ≈ $20,000(0.328509)
v ≈ $6,570.18
So, the value of the car after 5 years is approximately $6,570.18.
To find the value of the car after 8 years, you would use the same formula:
v = $20,000(1 - 0.21)^8
v ≈ $20,000(0.79)^8
v ≈ $20,000(0.117818)
v ≈ $2,356.36
So, the value of the car after 8 years is approximately $2,356.36.
The answer you obtained, $6,154.11, is close but not the correct value because you might have rounded off the intermediate calculations.