Question

A piece of equipment cost a certain factory ₹ 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?

Answer 1

Given : 

A piece of equipment cost a certain factory is 600,000 

To find : 

Value of the equipment at the end of 10 years 

It depreciates 15%, 13.5%, 12% in 1^st, 2^nd, 3^rd year and so on. 

This means price of equipment is depreciating in an A.P. A.P. will be 15, 13.5, 12,…………………………upto 10 terms 

Hence,

a = 15, 

d = 13.5 – 15 

= –1.5 

Formula used :

S_n = \(\frac{n}{2}\){2a + (n-1)d}

Where a is first term, d is common difference and n is number of terms in an A.P. 

Therefore, 

Total percentage of depreciation in 10 years,

Value of the equipment at the end of 10 years,

= 175 × 600 

= 105000

Hence, 

Value of equipment at the end of 10 years is Rs. 105000