# ACMGM094

## 2.2 Analysis of Compound Interest

### Compound Interest with Regular Additions or Withdrawals

Note: if you cannot remember the basic recursive formula for a compound interest system, revise notes for 2.1 Simple and Compound Interest.

• A compound interest system with regular additions or withdrawals has both a percentage increase/decrease and a fixed amount increase/decrease at each compounding period.
• This type of system can be modelled using the following recursive formula:
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## 2.1 Simple and Compound Interest

Note: the formulas used in this topic describe the simplest form of these systems. Future notes will analyse situations involving regular withdrawals or additions.

### Simple Interest

• Simple interest describes a system that increases or decreases by a fixed amount after each period of time. That amount is calculated as a percentage of the initial value of the system.
• Graphs for this type of system are linear.
• This type of system can be modelled using the following recursive formula:

A_{n+1}=I A_{0}+A_{n}

Where I is the interest rate as a decimal, A_{0} is the initial value and A_{n} is the value after n periods of time.

• A non-recursive formula can also be used:
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