Financial and Budgetary Calculations
Money in, money out
Budget questions combine percentages, rates and careful reading of tax and discount conventions. Distinguish gross (before deductions) from net (after deductions), cost from selling price, and markup from margin. Markup is a percentage of cost; margin is a percentage of selling price. Simple interest is principal × rate × time; compound interest applies the multiplier (1 + r)^n. A budget variance is actual minus planned, often expressed as a percentage of the plan. Per-capita figures divide a total by population, so a small percentage of a large base can exceed a large percentage of a small one.
Traps
Order matters: a discount followed by tax is not the same as tax followed by a discount, because the tax base changes. A 20% discount followed by a further 10% discount is an 18% total discount, not 30%. Tax brackets apply only to income within each band, not to the whole income at the top rate. Watch for monthly versus annual figures and for currency rounding at intermediate steps. “Percentage of budget” and “percentage-point change in the budget” are different measures.
Worked example
Gross pay is 3,200 per month. Tax is 20% on the first 2,000 and 40% on the excess. Tax = 0.20 × 2,000 + 0.40 × 1,200 = 400 + 480 = 880. Net pay = 3,200 − 880 = 2,320.
Rule of thumb: identify the base of every percentage - cost, price, income band or budget - before multiplying.