Question 1155467
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.
<a href = "https://debitoor.com/dictionary/reducing-balance-depreciation" target = "_blank">https://debitoor.com/dictionary/reducing-balance-depreciation</a>
<a href = "https://www.thehartford.com/business-insurance/strategy/depreciating-assets/reducing-balance-method" target = "_blank">https://www.thehartford.com/business-insurance/strategy/depreciating-assets/reducing-balance-method</a>
<a href = "https://www.thehartford.com/business-insurance/strategy/depreciating-assets/reducing-balance-method" target = "_blank">https://www.thehartford.com/business-insurance/strategy/depreciating-assets/reducing-balance-method</a>
<a href = "http://www.accioneduca.org/admin/archivos/clases/material/depreciation_1564412042.pdf" target = "_blank">http://www.accioneduca.org/admin/archivos/clases/material/depreciation_1564412042.pdf</a>