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# FM Withdrawal

## 4.3 Modelling Compound Interest Systems with Regular Withdrawals using Technology

Note: if you cannot remember how to model reducing balance relations with regular repayments, revise notes for 4.1 Modelling Compound Interest Systems with Regular Withdrawals.

### Guide to Analysing Compound Interest Equations with Regular Withdrawals using Technology (Casio Graphics Calculator)

Note: if you cannot remember how to use the Casio Financial Calculator, revise notes for 3.3 Modelling Reducing Balance Systems with Regular Repayments using Technology.

• The annual interest rate should be entered/calculated as a positive value.
• The initial value (PV) should be entered/calculated as a negative value (remember we justify this by saying we must lose this amount to create the account).
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## 4.2 Modelling Compound Interest Systems with Regular Withdrawals using Tables

Note: if you cannot remember how to model reducing balance systems with regular repayments, revise notes for 4.1 Modelling Compound Interest Systems with Regular Withdrawals.

### Guidelines to using a Table for Compound Interest Systems with Regular Withdrawals

• Tables provide a convenient method for analysing compound interest systems with regular withdrawals, especially when there are regular systemic changes (e.g. the interest rate or withdrawals change regularly).
• The columns of the table should list, the compounding period, withdrawal, interest earned, principal addition (i.e. the amount the system has increased/decreased during each compounding period) and the balance at the end of the compounding period.
• The principal addition can be calculated as follows:
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## 4.1 Modelling Compound Interest Systems with Regular Withdrawals

Note: if you cannot remember the recurrence relation formula for a compound interest system, revise notes for 2.2 Analysis of Compound Interest.

### Modelling using a Recurrence Relation

• A compound interest system with regular withdrawals describes a system which has a positive interest rate, and withdrawals (negative) made at the end of each compounding period.
• We can use the simple recursion formula to model this system:

A_{n+1}=d+(1+I) A_{n}

Where d<0 and I>0.

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