a brand new car that is originally valued at $25,000 depreciates by 8% per year. what is the value of the car after 6 years?
each year value = 0.92 value year before
v = Vi (0.92)^n
v = 25,000 (0.92)^6
13.000
To calculate the value of the car after 6 years, you'll need to apply the annual depreciation rate for each year.
Step 1: Calculate the depreciation amount for each year.
To find the depreciation amount for the first year, multiply the original value ($25,000) by the depreciation rate (8% or 0.08):
Depreciation amount for Year 1 = $25,000 * 0.08 = $2,000
Since the depreciation rate is constant, the depreciation amount for each subsequent year will be the same as for the first year ($2,000).
Step 2: Calculate the remaining value after each year.
To calculate the remaining value after each year, subtract the depreciation amount for that year from the original value.
Year 1:
Remaining value after Year 1 = $25,000 - $2,000 = $23,000
Year 2:
Remaining value after Year 2 = $23,000 - $2,000 = $21,000
Year 3:
Remaining value after Year 3 = $21,000 - $2,000 = $19,000
Year 4:
Remaining value after Year 4 = $19,000 - $2,000 = $17,000
Year 5:
Remaining value after Year 5 = $17,000 - $2,000 = $15,000
Year 6:
Remaining value after Year 6 = $15,000 - $2,000 = $13,000
Therefore, the value of the car after 6 years is $13,000.