Business Mathematics and Statistics: Interest, Break-even and Data
Arithmetic, interest and break-even
Business mathematics tests percentages, ratios, proportions, index numbers and the time value of money. Simple interest is I = P × r × t; compound interest uses A = P(1 + r/n)^(nt), so more frequent compounding raises the effective rate. Discounting reverses compounding: present value = future value ÷ (1 + r)^n.
Break-even analysis separates fixed and variable costs. Contribution per unit = selling price − variable cost per unit; break-even units = fixed costs ÷ contribution per unit. A trap is mixing units with sales values, or forgetting that contribution, not selling price, covers fixed costs.
Statistics
Measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation) summarise data. The mean is sensitive to outliers; the median is not. Standard deviation is in the same units as the data, variance in squared units. In probability, "and" often means multiplication and "or" addition; without replacement, the denominator falls after each draw.
Traps to watch
Correlation does not prove causation. Index numbers need a stated base year. Averages of percentages should be weighted by their bases, not simply averaged. Sampling bias undermines any conclusion drawn from a survey.
Worked example
Fixed costs are Ksh 120,000; selling price Ksh 50; variable cost Ksh 30. Contribution = Ksh 20 per unit. Break-even = 120,000 ÷ 20 = 6,000 units. At that level total contribution Ksh 120,000 exactly covers fixed costs, so profit is zero. Rule of thumb: check whether the answer should be in units or sales value (6,000 × Ksh 50 = Ksh 300,000).