Question 4 (d)

Years of use of a machine depreciated at 6% on the opening value

6 marks

Time to write: About 12 minutes
Topic: Depreciation and average due date

Question

Question 4 (d) · 6 marks

A machine depreciates at the rate of 6% of its value at the beginning of a year. It was purchased for ₹1,20,000 and the scrap value realized when sold was ₹57,110. Find the number of years the machine was used.

Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.

Before you write

Read off the question and its marks

12 minfor 6 marks

Read from the question

FindFormula first, then the working, then the answer with its unit (₹, %, units).

What the paper leaves open

The paper sets this part under the instruction to answer any three questions, and gives it 6 marks.

Write it in this order

Read the data; note exactly what is asked 1 min
1 Depreciation relation 2 marks 3 min
2 Logarithmic solution 3 marks 5 min
3 Number of years with check 1 mark 2 min
Check: arithmetic, units (₹, %), final answer underlined 1 min

123

Short on time? Step 2 carries 3 of the 6 marks: guard its minutes.

Try it first. About 12 minutes for 6 marks. Write it out, then open the solution.

Solution

Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.

Depreciation of 6% of the value at the beginning of each year leaves 94% of that value at the year end, so after n years the value is V = C(1 − 0.06)ⁿ, the compound-interest relation with a negative rate.

57,110 = 1,20,000 × (0.94)ⁿ ⟹ (0.94)ⁿ = 57,110/1,20,000 = 0.475917.

Taking logarithms: n = log 0.475917 / log 0.94 = (−0.322469)/(−0.026872) = 12.00.

The machine was used for 12 years.

Check: 1,20,000 × (0.94)¹² = 1,20,000 × 0.475920 = ₹57,110.44, i.e. ₹57,110 to the nearest rupee.

End of year	1	2	6	12
Value (₹)	1,12,800.00	1,06,032.00	82,784.37	57,110.44

Where the 6 marks sit

#	Component	Marks
1	Depreciation relation	2
2	Logarithmic solution	3
3	Number of years with check	1
	Total	6

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