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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1.1 Recurrence Relations and Sequences

Sequence

A list of numbers written down in succession.

Terms of a Sequence

The terms of a sequence can be identified by their term numbers.

The initial term or 0th term is A_{0}; The first term is A_{1};The second term is A_{2}.

A_{0}, A_{1}, A_{2}

The 𝑛th term is 𝑢; The term before the 𝑛th term is 𝑢; The term after the 𝑛th term is 𝑢.

A_{n-1}, A_{n}, A_{n+1}

Any letter, not just A, can represent the terms of a sequence.

Recurrence Relations

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