4.A machine costing Rs 80,000 would reduce to Rs 20,000 in 8 years. Find the rate of yearly depreciation, given that the depreciation is calculated using diminishing balances method.
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Answered by
3
20,000=80,000(1-d)^8
=> 8 log (1-d) = log 1 - log 4
=> log (1-d) = 0-0.6021/8
=> log (1-d) = -0.07525
=> (1-d) = Antilog (1.92475)
=> 1-d = 0.8389
=> d = 1-0.8389
=> d = 0. 1611
=> d = 16. 11 % ( ANSWER)
=> 8 log (1-d) = log 1 - log 4
=> log (1-d) = 0-0.6021/8
=> log (1-d) = -0.07525
=> (1-d) = Antilog (1.92475)
=> 1-d = 0.8389
=> d = 1-0.8389
=> d = 0. 1611
=> d = 16. 11 % ( ANSWER)
Answered by
1
Answer:
Original cost of machine, C = Rs. 80,000
Depreciated cost of machine after 8 years, D = Rs. 20,000
Time, n = 8 years
Let the rate of yearly depreciation be d.
Now, we have
D = C (1 - d)ⁿ
20,000 = 80,000 (1 - d)⁸
20,000/80,000 = (1 - d)⁸
1/4 = (1 - d)⁸
(1 - d)⁸ = 1/4
Taking log on both sides, we get
log [(1 - d)⁸] = log(1/4)
8 log (1 - d) = log 1 - log 4
8 log (1 - d) = 0 - 0.6021
8 log (1 - d) = -0.6021
log (1 - d) = -0.6021/8
log (1 - d) = - 0.07526
1 - d = antilog (-0.07526)
1 - d = 0.841
d = 1 - 0.841
d = 0.159
d % = 15.9 %
∴ The rate of yearly depreciation is d = 15.9 %.
Hence the rate of depreciation calculated using the diminishing balances method is 15.9 %.
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