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.