Question

A piece of equipment cost a certain factory $Rs.6,00,000$. If it depreciates in value, $15\%$ the first, $13.5\%$ the next year, $12\%$ the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

Answer 1

The piece of equipment depreciates $15\%$ in first year i.e., $\frac{15}{100}\times 600,000=Rs.90,000$

$\therefore$ Value depreciated in 1st year $=Rs.90,000$

The equipment depreciates at the rate $13.5\%$ in 2nd year i.e. $\frac{135}{1000}\times 600,000=Rs.81000$

$\therefore$ Value depreciated in 2st year $=Rs.81,000$

The value after 3rd year $=\frac{12}{100}\times 600000$

$\therefore$ Value depreciated in 3rd year $=Rs.72000$

The the series of depreciation become $90,000,81,000,72,\mathrm{000...}$ with,

$a=90,000$ and $d=-9000$

The total depreciation in 10 years

$\Rightarrow S_{10}=\frac{10}{2}[2\times 90000+(9\left)\right(-9000\left)\right]$

$=5[180000-81000]$

$=5\left[99000\right]$ $[\text{Using}{S}_n=\frac{n}{2}[2a+(n-1)d\left]\right]$

$=Rs.495,000$

$\therefore$ The cost of machine after 10 years

$=600,000-495,000=Rs.105,000$