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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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