Originally Posted by

**s_ingram** Hi William,

If a Car has value 100 today, in 1 year's time it will depreciate by 15% i.e. 100 * 0.15, So:

today 100

year 1 100 - 100 * 0.15

year 2 (100 - 100 * 0.15) - (100 - 100 * 0.15)* 0.15

etc

you can see the pattern: Where A is the present value and r is the rate

A(1 - r) - A(1 - r).r = A(1- r) [1 - r] = A(1 - r)(1 - r)

So in general the depreciation is:

$\displaystyle A(1 - r)^{y-1}$ where y is the period in years

So:

$\displaystyle A(1 - r) ^{y-1} = A / 2 \: :\$(to reduce the value by one half).

$\displaystyle (1 - r)^{y-1} = 0.5$

$\displaystyle (y - 1) log (1 - r) = log(0.5)$

$\displaystyle y = 1 + \frac{log(0.5)}{log(0.85)}$

period = 5.26 years