The formulas on your sheet
- Compound growth: A = P(1 + i)ⁿ. Compound decay: A = P(1 − i)ⁿ.
- Straight-line depreciation: A = P(1 − in).
- Effective rate: 1 + i_eff = (1 + i_nom/m)^m.
- Future value annuity: F = x[(1 + i)ⁿ − 1]/i.
- Present value annuity: P = x[1 − (1 + i)⁻ⁿ]/i.
Worked example: a home loan
A loan of R900 000 is repaid over 20 years with monthly payments at 11% per year compounded monthly. Here i = 0.11/12 and n = 240. Using P = x[1 − (1 + i)⁻ⁿ]/i, x = 900 000 × i / [1 − (1 + i)⁻²⁴⁰] ≈ R9 290 per month.
Keep full accuracy in your calculator and round only the final answer to the nearest cent.
Worked example: outstanding balance
The balance after 5 years (60 payments) is the present value of the remaining 180 payments: P = x[1 − (1 + i)⁻¹⁸⁰]/i. Substituting x ≈ 9 290 gives a balance of roughly R806 000.
A common alternative method is future value of the loan minus future value of the payments made. Either method earns full marks if the timeline is correct.
Timeline rules that prevent errors
- Draw a timeline and mark the first and last payment.
- Future value annuities count payments up to the end; present value annuities count payments from one period after the loan starts.
- A deferred payment means fewer payments, not a different formula.
- Convert the interest rate to the payment period before substituting.
Official sources
Check the latest information with your school and the Department of Basic Education.