Question

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.

Answer 1

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)

Answer 2

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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