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:

where y is the period in years

So:

(to reduce the value by one half).

period = 5.26 years