Question

An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

Answer 1

In the given question, the formula representing depreciation of the car is

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

And it is given that,

The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year.

Substituting the values, we will get

$12282.50 = 20000(1-0.15)^t \\ 12282.50 = 20000(0.85)^t$

Dividing both sides by 20000, and taking log, we will get

$log ( \frac{12282.50}{20000}) = t log 0.85$

Dividing both sides by log(0.85), we will get

$-0.21174322= -0.07058107t$

Therefore,

$t=3$

Answer 2

The answer is 3 years