A piece of equipment cost a certain factory Rs. 600,000. 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?

A piece of equipment cost a certain factory Rs. 600,000. It depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on.

To do:

We have to find its value at the end of 10 years. Solution:

Cost of a piece of equipment $= Rs.\ 600,000$ Rate of depreciation for the first year $= 15 \%$ Rate of depreciation for the second year $= 13.5 \%$ Rate of depreciation for the third year $= 12.0 \%$

The rate of depreciation is in A.P., where

First term $a = 15$ and common difference $d = 13.5 – 15.0 = -1.5$

Number of terms $n = 10$

We know that,

$S_n=\frac{n}{2}[2 a+(n-1) d]$

Therefore,

Total depreciation$ \%=\frac{10}{2}[2 \times 15+(10-1)(-1.5)]$

$=5[30+9 \times(1.5)]$

$=5[30-13.5]$

$=5 \times 16.5$

$=82.5 \%$

This implies,

Total depreciation $=Rs.\ \frac{600000 \times 82.5}{100}$

$=Rs.\ 495,000$
Its value at the end of 10 years \( =Rs.\ 600,000-Rs.\ 495,000=Rs.\ 105,000 \)

Therefore, its value at the end of 10 years is Rs. 105,000.