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.