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# FM Predicting Value

## 2.4 Predicting Future Values for Compound Interest Loans and Investments

### Predicting Future Values involving Compound Interest

• Predicting the value of a compound interest system after a large number of compounding periods is a long and tedious process using recursion. Fortunately, for systems which do not involve regular additions or withdrawals, we can use the convenient formula:

A_{n}=\left(1+\frac{r}{100}\right)^{n} A_{0}

Where A_{n} is the amount after n compounding periods, r is the interest as a percentage and A_{0} is the initial value.

• When dealing with systems which do have regular additions or withdrawals, the only method we have (in the scope of this course) is recursion.
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## 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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