Question

A new car is purchased for 24000 dollars. The value of the car depreciates at 15% per year. To the nearest tenth of a year, how long will it be until the value of the car is 10000 dollars

Answer 1

The value of the car will be $10000 after 2.5 years

The cost price of the car = $24000

Rate of depreciation, r = 15%

r  =  15/100

r  =  0.15

The final value of the car after depreciation, A = $10000

To get the time for depreciation, use the formula below and solve for t

$A=P(1-r)^t$

Substitute P = 24000, A = 10000, and r = 0.15 into the equation above

$10000=15000(1-0.15)^t\\\\\frac{10000}{15000} = 0.85^t\\\\0.85^t=0.67\\\\t (ln0.85)=ln0.67\\\\-0.163t=-0.4\\\\t=\frac{-0.4}{-0.163} \\\\t=2.5$

The value of the car will be $10000 after 2.5 years

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