Question

An automobile, having an original value of $18,000 when new, depreciates at a rate of 18% per year. Determine, to the nearest tenth of a year, how long it takes for the value of the automobile to decrease to $1,000.

Answer 1

Answer:

14.6 years

Explanation:

Applying an early depreciation rate 'r = 18%', the value of an automobile originally valued at $18,000, after 't' years, is given by:

$V(t)=\ 18,000*(1-r)^t}$

The number of years required for which V(t) = $1,000 is:

$\ 1,000=\ 18,000*(1-0.18)^t\\ln(\frac{1,000}{18,000})=t*ln(0.82)\\ t=\frac{ln(0.05555555)}{ln(0.82)} \\t=14.6\ years$

It will take 14.6 years for the value of the automobile to decrease to $1,000.