Home » Further Maths Unit 3 & 4 » A2 - Recursion and Financial Modelling » 3.1 Modelling Reducing Balance Systems with Regular Repayments

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.

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