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).
Read More »4.3 Modelling Compound Interest Systems with Regular Withdrawals using Technology

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