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?
Given:
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.
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