Reducing Balance Depreciation

Reducing balance depreciation refers to a decrease of an item’s book value by a rate (that is a percentage of the previous book value of the good) each time interval.

The Formula

BV_T=P(1-\dfrac r{100})^T

Example 1

Nick purchased a new computer for $1,300. He depreciates the computer using the reducing balance method at a rate of 15% per annum. What will the computer’s total depreciation and book value be after three years?

State the information we are provided with in the question.

P=1,300
r=15
T=3

Substitute these values into the formula to find the book value after three years.

BV_T=P(1-\dfrac r{100})^T
BV_3=1,300(1-\dfrac 15{100})^3
BV_3=1,300(0.85)^3
BV_3=798.3625

Use the book value to calculate the total depreciation.

Total depreciation =P-BV
Total depreciation =1,300-798.3625
Total depreciation =501.6375

The book value of the computer after three years will be $798.36 and the total depreciation will be $501.64.

Remember

  • Reducing balance depreciation is also known as diminishing value depreciation so look out for both of these terms in the question.
  • When an item’s book value equals zero, it will be written off.
  • Scrap value refers to the book value of the item when it will no longer be used.

See also

Compound Interest
Effective Interest Rate
Straight Line Depreciation
Unit Cost Depreciation