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?

5 years

Step-by-step 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.