A Piece Of Equipment Costs Rs 600000 If It Depreciates In Value 1 The First Year 135 Next 12 Third Year So On What Will Be Its Value At End Of 10 Years All Percentages Applying To The Original Costs?
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Question:
A Piece Of Equipment Costs Rs 600000 If It Depreciates In Value 1 The First Year 135 Next 12 Third Year So On What Will Be Its Value At End Of 10 Years All Percentages Applying To The Original Costs?
Answer:
values are 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 =
\frac{17.5}{100 } \times 600000 = 105000
100
17.5×600000=105000..
Qᴜᴇꜱᴛɪᴏɴ :
❥ A Piece Of Equipment Costs Rs 600000 If It Depreciates In Value 1 The First Year 135 Next 12 Third Year So On What Will Be Its Value At End Of 10 Years All Percentages Applying To The Original Costs ?
ᴀɴꜱᴡᴇʀ :
➯ If you look at depreciation values year-wise, you will find there is a definite pattern i.e., in the first year, the depreciation value is 15%, second year 13.5%, third year 12% means the pattern is in Arithmatic Progression(AP), where the common difference is - 1.5% per year i.e., reduction by 1.5% every year .
➯ Now, applying AP formula, the value of depreciation at 10th year
= 15 + (10 - 1) * (-1.5) = 1.5%
➯ So, the series is :
15%, 13.5%, 12%, ………..1.5%
➯ The sum of all the depreciation values
= 15 * (15 + 1.5) / (2 * 1.5)
= 82.5% till the end of 10th year
➯ So, Left over values
= 100 - 82.5 = 17.5%
➯ Hence, remaining value after end of 10th year
= 600000 * 17.5/100
= $ 105000 Ans.
Hope it helps uhh !!