A machine is deprecated at the rate of 20% on reducing balance. The original cost of the machine was ₹ 1,00,000 and its ultimate scrap value was ₹ 30,000. The effective life of the machine is
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The machine is depreciated at the rate of 20% on reducing balance. The original lot of machine was Rs.100000 and the estimated scrap value is Rs.30000. What is the effective life of machine in years?
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Satya Parkash Sud
, former Professor at Himachal Pradesh University Shimla (1986-2002)
Answered Jun 10, 2021 · Author has 4.5K answers and 11.9M answer views
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
The effective life of machine in years is about 5 year and 5 months.