Unit cost depreciation is where the book value of an item is reduced based on how much it is used.

## The Formulas

Current book value $=previous\hspace{0.1cm}book\hspace{0.1cm}value-depreciation$

Amount of depreciation $=amount\hspace{0.1cm}of\hspace{0.1cm}use\times rate$

Rate of depreciation $=\dfrac {amount\hspace{0.1cm}of\hspace{0.1cm}depreciation}{amount\hspace{0.1cm}of\hspace{0.1cm}use}$

### Example 1

A taxi was purchased for $35,000 and depreciates by an average of 23.6 cents per kilometre travelled. In one year the car is driven 22,461 kilometres. a) What is the annual depreciation for this one year? Use the amount of depreciation formula. Make sure that you change the rate from cents to dollars. Amount of depreciation $=amount\hspace{0.1cm}of\hspace{0.1cm}use\times rate$ Amount of depreciation $=22,461\times 0.236$ Amount of depreciation $=5,300.796$ The taxi depreciates by$5,300.80 in this particular year.

b) If the taxi has a scrap value of \$15,000, what is its useful life (correct to the nearest kilometre)?

Find how much the taxi would need to depreciate by.

Total depreciation $=35,000-15,000$
Total depreciation $=20,000$

Now use this value to calculate the distance that would need to be travelled.

Rate of depreciation $=\dfrac {amount\hspace{0.1cm}of\hspace{0.1cm}depreciation}{amount\hspace{0.1cm}of\hspace{0.1cm}use}$
Rate of depreciation $=\dfrac {20,000}{0.236}$
Rate of depreciation $=84,745.7627$

The taxi has a useful life of 84,746 kilometres.
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