Business Mathematics: Counting and Commercial Arithmetic
Domain 4, Business Mathematics, focuses on counting and commercial arithmetic: permutations and combinations, simple and compound interest, and effective rates. Questions often combine “arrange or select” decisions with a financial formula.
Core rules
- Fundamental principle: if one task has m outcomes and a second has n, the pair has mn outcomes.
- nPr = n!/(n−r)! counts ordered selections of r from n distinct items. nCr = nPr/r! = n!/[r!(n−r)!] counts unordered selections.
- Simple interest = P×r×t. Compound amount = P(1+r)^t for annual compounding; CI = amount − P. For m compounds per year, use rate r/m and mt periods.
- Effective annual rate = (1 + r/m)^m − 1. Use it to compare nominal rates with different compounding frequencies.
Worked example
From five distinct letters, the number of three-letter arrangements without repetition is 5P3 = 5!/(5−3)! = 5×4×3 = 60. If order does not matter, the number of three-letter selections is 5C3 = 10. For finance, P = 1,000 at 10% for 2 years: SI = 1,000×0.10×2 = 200; CI = 1,000(1.10)² − 1,000 = 1,210 − 1,000 = 210. The 10 difference is interest on the first year’s interest.
Traps
Do not use nPr when the question says “committee” or “selection”; order is irrelevant for combinations. In CI, do not multiply the simple-interest amount by the number of years. Convert percentages to decimals and keep time in the same unit as the rate. For “at least one” counting, the complement is often shorter.