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Question

A piece of equipment costsRs6,00,000 in a certain factory. If it depreciates in value15% the first year, 13.5% the next year, 12%the third year, and so on. What will be its value at the end of10 years, all percentages applying to the original costs ?


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Solution

Finding the equipment cost:

The cost of equipment =Rs6,00,000

Step 1 - Finding the type of series

The value depreciates as

15%,13.5%,12%,--------

Percentage of depreciation in the first year =15%

Percentage of depreciation in the second year =13.5%

Percentage difference = 15%-13.5%

=-1.5%

Percentage of depreciation in the third year =12%-13.5%

=-1.5%

Since, the percentage of depreciation is constant =-1.5%

Therefore, the series is in arithmetic progression.

Step 2- Value of equipment after 10years

Since the rate of depreciation is in arithmetic progression

So, the first term a=15%

Common difference d=-1.5%

Number of terms n=10

Total percentage depreciation in 10 years

s=n22a+n-1×d

s=1022×15+10-1×-1.5

s=530+9×-1.5

s=530-13.5

s=5×16.5

s=82.5

Therefore, percentage depreciation in 10 years =82.5%

Value of depreciation =100-depreciation%100× cost of equipment

=100-82.5100×6,00,000=17.5100×6,00,000=17.5×6000=Rs105000

Hence, the value of the equipment after 10 years is Rs105000.


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