Financial Mathematics: Earning, Spending and Investing
What you must understand
Financial mathematics covers wages and salaries, overtime, commission, leave loading, tax, simple and compound interest, depreciation, and budgeting. You need to convert between pay periods (weekly, fortnightly, monthly, annual), calculate gross and net pay, apply the compound interest formula A = P(1 + r)ⁿ, and use straight-line and declining-balance depreciation. You should also interpret tables such as tax brackets and understand the effect of rounding on money answers.
Traps that appear in questions
- Pay period conversion. A fortnightly pay is not half a monthly pay; there are 26 fortnights but 12 months in a year. Annual salary ÷ 26 gives fortnightly pay; ÷ 12 gives monthly pay.
- Overtime rates. Time-and-a-half means 1.5 × the normal hourly rate for the overtime hours only, not for all hours worked.
- Interest rate as a decimal. In A = P(1 + r)ⁿ, r must be expressed as a decimal per compounding period; if interest is monthly, divide the annual rate by 12 and multiply n by 12.
- Depreciation direction. Declining-balance depreciation uses (1 − r)ⁿ, not (1 + r)ⁿ; straight-line subtracts the same amount each year.
- Rounding money. Round to the nearest cent at the end, and do not round intermediate rates.
Worked example
$4500 is invested at 4.2% per annum compounding annually for 3 years. A = 4500(1 + 0.042)³ = 4500 × 1.13137 ≈ $5091.17. Interest earned = 5091.17 − 4500 = $591.17. Compare with simple interest: I = Prn = 4500 × 0.042 × 3 = $567, which is less, showing the effect of compounding.
Rule of thumb
Decide the compounding period first, adjust r and n to match it, then substitute; and always sanity-check that net pay is less than gross pay and that interest earned is positive.