Dan's car depreciates at a rate of 14% per year. By what percentage has Dan's car depreciated after 6 years? Give your answer to the nearest percent.
Answers
Dan's car depreciated by 54% after 6 years.
Step-by-step explanation:
Price of a depreciating asset:
The price of a depreciating asset after t years is given by:
P(t) = P(0)(1-r)t
In which P(0) is the initial price and r is the decrease rate, as a decimal.
Dan's car depreciates at a rate of 12% per
year.
This means that r = 0.12, so
P(t) = P(0)(1-r)t
P(t) = P(0) (10.12)
P(t) = P(0) (0.88)
By what percentage has Dan's car depreciated after 6 years?
Relative to the initial value, the value after 6 years is given by:
P(6)=P(0) (0.88)6 = 0.46P(0)
The value after 6 years if 0.44 of the initial value, that is, there was a depreciation of 100 - 46 = 54%.
P(6)=P(0) (0.88)6 = 0.46P(0)
The value after 6 years if 0.44 of the initial value, that is, there was a depreciation of 100 - 46 = 54%.
Dan's car depreciated by 54% after 6 years.