Question

The value of a machine depreciated by $10$% per year during the first two years and $15$% per year during the third year. Express the total depreciation of the machine, as per cent, during the three years.

Answer 1

Let the original value be be $M$
After being depreciated at $R=10$ %, for $2$ years we have its value $=OriginalValue\times {(1-\frac{R}{100})}^N=M\times {(1-\frac{10}{100})}^2=M\times 0.9\times 0.9=Rs0.81M$
For the third year, at $R=15$ %, we have its value still reduced to
$=0.81M\times {(1-\frac{15}{100})}^1=0.81M\times 0.85=Rs0.6885M$
So, total % change in $3$ years $=\frac{M-0.6885M}{M}\times 100=31.15$ %