A piece of equipment cost a certain factory Rs 60,000. 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?
Answers
Answer:
The cost of a piece of equipment at the end of 10 years is ₹ 1,05,000.
Step-by-step explanation:
Given :
Cost of a piece of equipment (original cost) = ₹ 6, 00, 000
The value depreciate in 1 year = 15%
⇒ The value of the equipment after first year = 15/100 × 6,00, 000
= ₹ 90, 000
The value depreciate in 2 year = 13.5%
⇒ The value of the equipment after second year = 13.5/100 × 6,00,000
= ₹ 81,000
The value depreciate in 3 year = 12%
⇒ The value of the equipment after third year = 12/100 × 6,00,000
= ₹ 72, 000
Here , A.P. is ₹ 90000, ₹ 81000, ₹ 72000,…….
Then , first term , a = 90000 , common difference,d = 81000 – 90000 = - 9000
By using the formula, Sn = n/2 [2a + (n – 1) d]
S10 = 10/2 [2(90000) + (10 - 1) ( - 9000)]
S10 = 5[180000 + 9 × (- 9000)]
S10 = 5 [180000 - 81000]
S10 = 5 [99000]
S10 = 495000
The cost of a piece of equipment at the end of 10 years = original cost – depreciation
= ₹ 6,00,000 – ₹ 4,95,000
= ₹ 1,05,000
Hence, the cost of a piece of equipment at the end of 10 years is ₹ 1,05,000.
HOPE THIS ANSWER WILL HELP YOU….
Step-by-step explanation:
I m taking values as 15%, 13.5% and 12%
Let the cost of an equipment be Rs. 100.
Now the percentages of depreciation at the end of 1st,2nd,3rd years are 15, 13.5,12, which are in A.P., with a=15 and d= -1.5.
Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5 (Sum of 10 terms of the AP)
Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5
Thus the required total value =
