SOLUTION: 6. A mainframe computer whose cost is k220 will depreciate to a scrap value of k12 in 5 years. what is the depreciation rate by use of the reducing balance method. [4 marks]

Question 1155467: 6. A mainframe computer whose cost is k220 will depreciate to a scrap value of k12 in 5
years. what is the depreciation rate by use of the reducing balance method. [4 marks]
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
there are different ways to calculate reducing balance method.
one of the simples, and the one i'll use her, is to depreciate by a set percentage each year.
your initial value is 220 and your residual value is 12 in 5 years.
the formula to use would be f = p * (1 + r) ^ n
f is the future value (12)
p is the present value (220)
r is the interest rate per time period ( per year for this problem)
n is the number of time period (in years for this problem)
the formula becomes 12 = 220 * (1 + r) ^ 5.
divide both sides of the formula by 12 to get 12 / 220 = (1 + r) ^ 5.
take the fifth root of both sides of the equation to get (12 / 220) ^ (1/5) = 1 + r.
subtract 1 from both sides of the equation to get (12 / 220) ^ (1/5) - 1 = r.
solve for r to get r = -.4410773454.
confirm by replacing r in the formula with that to get:
12 = 220 8 (1 - .4410773454) ^ 5 to get 12 = 12.
this confirms the value of r is correct.
your solution is that the depreciation rate is -44.10773454% per year. *****
your depreciation schedule would look like this.
start with 220
after 1 year, value is 122.962984
after 2 years, value is 68.72679743
after 3 years, value is 38.41296406
after 4 years, value is 21.46987584
after 5 years, value is 12
note that this is only one of several reducing balance methods of depreciation.
here's some references.
https://debitoor.com/dictionary/reducing-balance-depreciation
https://www.thehartford.com/business-insurance/strategy/depreciating-assets/reducing-balance-method
https://www.thehartford.com/business-insurance/strategy/depreciating-assets/reducing-balance-method
http://www.accioneduca.org/admin/archivos/clases/material/depreciation_1564412042.pdf

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