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FM Interest Rate

5.3 Modelling Annuity Investments using Technology

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

Guide to Analysing Annuity Investments 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 investment).
  • The payment (PMT) (i.e. the amount withdrawn) should be entered/calculated as negative (we can justify this by saying we lose this amount per compounding period to the investment)
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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

4.1 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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3.1 Modelling Reducing Balance Systems with Regular Repayments

Note: if you cannot remember what a reducing balance system is, revise notes for 1.2 Forms of Depreciation and 1.3 Predicting Future Values for Depreciation Systems.

Modelling using Recursion Relations

  • A reducing balance system with regular repayments describes a system which has a negative interest rate, and positive deposits 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 »3.1 Modelling Reducing Balance Systems with Regular Repayments