# ACMGM099

## 5.2 Modelling Annuity Investments using Tables

Note: if you cannot remember how to model reducing balance systems with regular repayments, revise notes for 5.1 Modelling Annuity Investments.

### Guidelines to use a Table for Annuity Investments

• Tables provide a convenient method for analysing annuity investments, especially when there are regular systemic changes (e.g. the interest rate or repayments change regularly).
• The columns of the table should list, the compounding period, payment, interest earned, principal addition (i.e. the amount the system has increased during each compounding period) and the balance at the end of the compounding period.
• The principal addition can be calculated by as follows:
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## 5.1 Modelling Annuity Investments

### Modelling using Recursion Relations

• An annuity investment describes a system which has a positive interest rate, and positive deposits made at the end of each compounding period.
• We can use the simple recursion formula to model this system:
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## 4.4 Annuities and Perpetuities

### Annuities

Note: if you cannot remember what a compound interest system is, revise notes for 2.1 Simple and Compound Interest.

• Compound interest systems with regular payments or withdrawals are often known as annuities.

### Perpetuities

• Perpetuities are a special case of annuity, which does not change value.
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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:
Read More »4.2 Modelling Compound Interest Systems with Regular Withdrawals using Tables

## 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.

Read More »4.1 Modelling Compound Interest Systems with Regular Withdrawals