Question

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 soon. What will be its value at the end of 10 years, all percentages applying to the original cost?

Answer 1

Given: 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 soon. 

To find: The value at the end of 10 years if all percentages applying to the original cost. 

Solution:Cost of equipment = 6, 00, 000 

In 1 year the value depreciate by 15% 

⇒ The value of the equipment after first year= 6, 00, 000 x \(\frac{15}{100}\) = 90, 000 

In 2 year depreciate by 13.5% 

⇒ The value of the equipment after second year= 6, 00, 000 x \(\frac{13.5}{100}\) = 81, 000 

In 3 year depreciate by 12% 

⇒ The value of the equipment after third year= 6, 00, 000 x \(\frac{12}{100}\) = 72, 000 

Now A.P. is 90000, 81000, 72000,…

So, common difference = 81000 – 90000 = -9, 000 

We have to find total depreciation for 10 years,

Since the value of depreciation is constant in any consecutive years i.e its value is -9000. 

So to find the depreciation after ten years we will use the formula:

S_n= \(\frac{n}{2}\)[2a + (n – 1) d] 

S₁₀= \(\frac{10}{2}\)[2(90, 000) + (10 – 1) (-9000)] 

S₁₀= 5 [180000 + 9 x (-9000)] 

S₁₀= 5 [180000 – 81000] 

S₁₀= 5 [99000] = 495000 

Hence, cost of equipment at the end of 10 years = original cost – depreciation 

= 6, 00, 000 – 4, 95, 000 = Rs.1, 05, 000