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A machine is depreciated at the rate of 20% on reducing balance. The original cost of the machine was Rs. 100000 and its ultimate scrap value was Rs. 30000. The effective life of the machine is
- a)4.5 years (appx.)
- b)5.4 years (appx.)
- c)5 years (appx.)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A machine is depreciated at the rate of 20% on reducing balance. The o...
Cost of machine (P) = Rs 1,00,000
Scrap value (A) = Rs 30,000
Rate of Depreciation = 20% per annum on reducing value
The effective life of the machine in years is the number of years in which P (Rs 1,00,000) would reduce to A (scrap value Rs 30,000) reducing at the rate of 20% per annum of the value at the start of that year year.
Value of the machine at time t= 0 years = P
The depreciated cost at end of one year = P[1 — 20%] = P[1 — 0.2] = P × 0.8
At the end of second year = P × 0.8²
At the end of 3rd year = P × 0.8³
And so on.
Let after n years the value depreciate to scrap value. We are required to find n.
P(0.8)^n = A
1,00000 (0.8)^n = 30,000
=> (0.8)^n = (30,000)/(1,00,000) = 0.3
Taking log of both sides
n log (0.8) = log (0.3)
=>n × (-0.09691) = (-0.52288)
=> n = (-0.52288)/(-0.09691)= 5.396 year ~5.4 years
Most Upvoted Answer
A machine is depreciated at the rate of 20% on reducing balance. The o...
A machine deprecated at the rate of 20% on reducing balance.
The original cost of machine is ₹ 1,00,000.
At the end of
First year : 1,00,000 - (1,00,000 × 20%)
= 1,00,000 - 20,000
= 80,000
Second year : 80,000 - (80,000 × 20%)
= 80,000 - 16,000
= 64,000
Third year : 64,000 - (64,000 × 20%)
= 64,000 - 12,800
= 51,200
Fourth year : 51,200 - (51,200 × 20%)
= 51,200 - 10,240
= 40,960
Fifth year : 40,960 - (40,960 × 20%)
= 40,960 - 8,192
= 32,768
Sixth year : 32,768 - (32,768 × 20%)
= 32,768 - 6553.6
= 26,214.4
The ultimate scrap value of machinery is ₹ 30,000
At the end of Fifth year, the value of machinery is ₹ 32,768.
At the end of 5years, 6 months (approx.)
= 32,768 × 20/100 × 5.0685/12
= 2,768
Then, the scap value of machinery is :
>>> 32,768 - 2,768 = 30,000
The ultimate life of machinery is :
>>> 5.4 years (appx.)
>>> Option B
The original cost of machine is ₹ 1,00,000.
At the end of
First year : 1,00,000 - (1,00,000 × 20%)
= 1,00,000 - 20,000
= 80,000
Second year : 80,000 - (80,000 × 20%)
= 80,000 - 16,000
= 64,000
Third year : 64,000 - (64,000 × 20%)
= 64,000 - 12,800
= 51,200
Fourth year : 51,200 - (51,200 × 20%)
= 51,200 - 10,240
= 40,960
Fifth year : 40,960 - (40,960 × 20%)
= 40,960 - 8,192
= 32,768
Sixth year : 32,768 - (32,768 × 20%)
= 32,768 - 6553.6
= 26,214.4
The ultimate scrap value of machinery is ₹ 30,000
At the end of Fifth year, the value of machinery is ₹ 32,768.
At the end of 5years, 6 months (approx.)
= 32,768 × 20/100 × 5.0685/12
= 2,768
Then, the scap value of machinery is :
>>> 32,768 - 2,768 = 30,000
The ultimate life of machinery is :
>>> 5.4 years (appx.)
>>> Option B
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Community Answer
A machine is depreciated at the rate of 20% on reducing balance. The o...
Given:
Original cost of machine = Rs. 100000
Ultimate scrap value = Rs. 30000
Rate of depreciation = 20% on reducing balance
To find: Effective life of machine
Formula:
Depreciation = (Original cost - Scrap value) x Rate of depreciation
Effective life = Original cost / Annual depreciation
Calculation:
Annual depreciation = Original cost x Rate of depreciation
= Rs. 100000 x 0.2
= Rs. 20000
Let's assume the effective life of the machine is n years.
After n years, the book value of the machine will be equal to its scrap value.
So, we can write:
(Original cost - Depreciation for n years) = Scrap value
Rs. 100000 - Rs. (20000 x n) = Rs. 30000
Rs. 70000 = Rs. 20000 x n
n = 3.5 years
But this is the effective life of the machine assuming straight-line depreciation. Since the machine is depreciated at the rate of 20% on reducing balance, its effective life will be lesser than 3.5 years.
To calculate the effective life based on reducing balance depreciation, we can use the following formula:
Effective life = ln (Scrap value / Original cost) / ln (1 - Rate of depreciation)
where ln is the natural logarithm.
Effective life = ln (30000 / 100000) / ln (1 - 0.2)
= ln (0.3) / ln (0.8)
= 5.42 years (approx.)
Therefore, the effective life of the machine is approximately 5.4 years. Option (b) is the correct answer.
Original cost of machine = Rs. 100000
Ultimate scrap value = Rs. 30000
Rate of depreciation = 20% on reducing balance
To find: Effective life of machine
Formula:
Depreciation = (Original cost - Scrap value) x Rate of depreciation
Effective life = Original cost / Annual depreciation
Calculation:
Annual depreciation = Original cost x Rate of depreciation
= Rs. 100000 x 0.2
= Rs. 20000
Let's assume the effective life of the machine is n years.
After n years, the book value of the machine will be equal to its scrap value.
So, we can write:
(Original cost - Depreciation for n years) = Scrap value
Rs. 100000 - Rs. (20000 x n) = Rs. 30000
Rs. 70000 = Rs. 20000 x n
n = 3.5 years
But this is the effective life of the machine assuming straight-line depreciation. Since the machine is depreciated at the rate of 20% on reducing balance, its effective life will be lesser than 3.5 years.
To calculate the effective life based on reducing balance depreciation, we can use the following formula:
Effective life = ln (Scrap value / Original cost) / ln (1 - Rate of depreciation)
where ln is the natural logarithm.
Effective life = ln (30000 / 100000) / ln (1 - 0.2)
= ln (0.3) / ln (0.8)
= 5.42 years (approx.)
Therefore, the effective life of the machine is approximately 5.4 years. Option (b) is the correct answer.
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A machine is depreciated at the rate of 20% on reducing balance. The original cost of the machine was Rs. 100000 and its ultimate scrap value was Rs. 30000. The effective life of the machine isa)4.5 years (appx.)b)5.4 years (appx.)c)5 years (appx.)d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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