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# FM Linear Depreciation

## 1.3 Predicting Future Values for Depreciation Systems

Note: if you cannot remember how to model each of these types of depreciation using recurrence relation formulas and how they appear graphically, revise notes for 1.2 Forms of Depreciation.

### Predicting Values for Flat Rate Depreciation

• You may notice from the flat rate depreciation formula that this represents a system that increases by a value of d per unit in time (month, year, etc.), starting from the initial value; A_{0}. Thus, we can also express this relationship as the linear formula:

A=A_{0}+d t

Where t is the number of periods which have passed.

• This is equivalent to a linear relation with a slope of d, and a y-intercept of A_{0}.
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## 1.2 Forms of Depreciation

### Flat Rate Depreciation

• Flat rate depreciation occurs when the value of an asset decreases by a fixed amount every period (i.e. no interest occurs).
• Graphs of flat rate depreciation are linear.
• The recurrence relation formula describing flat rate depreciation is:

A_{n+1}=d+A_{n}

Note: as this is depreciation: d<0. Consequently, any graphs showing flat rate depreciation will have a negative slope.

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