Financial Arithmetic
Mastering financial maths starts with the basics. This section covers the essential percentage calculations for mark-ups, discounts, and GST, which are the building blocks for more complex financial models.
Percentage Change Calculator
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Introduction to Sequences
A recurrence relation defines the next term in a sequence based on the previous term. This is the core concept for modelling financial growth and decay step-by-step. Use the simulator below to see how it works.
CAS Sequence Simulator
Generated Sequence:
Arithmetic Sequences
Arithmetic sequences model linear growth or decay, where a fixed amount (the common difference, *d*) is added or subtracted each period. This applies to simple interest and flat-rate depreciation.
Simple Interest
Recurrence Rule: Vโ = P, Vโโโ = Vโ + d
Explicit Rule: Vโ = Vโ + n × d
Flat-Rate Depreciation
Recurrence Rule: Vโ = P, Vโโโ = Vโ – d
Explicit Rule: Vโ = Vโ – n × d
Geometric Sequences
Geometric sequences model exponential growth or decay, where the value is multiplied by a fixed factor (the common ratio, *R*) each period. This applies to compound interest and reducing-balance depreciation.
Compound Interest
Recurrence Rule: Vโ = P, Vโโโ = R × Vโ
Explicit Rule: Vโ = Rโฟ × Vโ
Reducing-Balance Depreciation
Recurrence Rule: Vโ = P, Vโโโ = R × Vโ
Explicit Rule: Vโ = Rโฟ × Vโ
Comparing Models
Visually comparing financial models reveals their long-term behaviour. Use the tool below to see how a compound interest investment (exponential) dramatically outperforms simple interest (linear) over time.
Study Summary & Checklist
Use this checklist to track your understanding of the key skills for this topic. The table below provides a quick reference for the core formulas.
Key Skills Checklist
Formula Summary
| Model | Recurrence Rule | Explicit Rule (Vโ) |
|---|---|---|
| Arithmetic | Vโโโ = Vโ + d | Vโ + n × d |
| Geometric | Vโโโ = R × Vโ | Rโฟ × Vโ |
