Question

Keaton bought a new Jeep for $32,000. The value of the car will depreciate at a rate of 8.5% per year. Growth or decay? What will the car be worth in 5 years? When will the car be worth half of what Carson paid?

Answer 1

Part a)

Price of car is $32,000 and the value of Car is depreciating at a rate of 8.5% per year. This means the worth of car is decreasing. Hence it is a decay.

Part b)
Worth of car in 5 years.

Current Price = P = $32000
Decay rate = r = 0.085
Time = t = 5 years

Formula to be used:

$A=P(1-r)^{t} \\ \\ A=32000(1-0.085)^{5} \\ \\ A=20523.69$

This means, the worth of car after 5 years will be reduced to $20,523.69

Part c)
When the car will be worth half of its original amount.

Half amount = $16,000
Using the values in above formula, we get

$16000=32000(1-0.085)t^{2} \\ \\ 0.5=(0.915)^{t} \\ \\ t=7.8$

This means, after 7.8 years the car be worth half of what Carson paid