Question

You bought your car for $12500 and it is depreciating at 13% per year. How long until it is only worth half of what you paid for it? What is your answer to the nearest year?

Answer 1

5 years

Explanation:

We are given;

• Initial value of the car = $12,500
• Rate of Depreciation = 13% per year
• New value (after depreciation) = $6,250 (half the initial value)

We are required to determine the time taken for the value of the car to depreciate to half the original value.

• We need to know the depreciation formula;
• New value = Initial value ( 1 - r/100)^n

Therefore;

$6,250 = $12,500(1 - r/100)^n

0.5 = (1 - 13/100)^n

0.5 = 0.87^n

Introducing log on both sides;

log 0.5 = n log 0.87

Therefore;

n = log 0.5 ÷ log 0.87

= 4.977

= 5 years

Therefore, it takes 5 years for the value of the car to depreciate to half the initial value.