Financial Mathematics for Matric Maths

Key concepts

• A = P(1 + i)ⁿ and A = P(1 − i)ⁿ
• Future value annuity: F = x[((1 + i)ⁿ − 1) / i]
• Present value annuity: P = x[(1 − (1 + i)⁻ⁿ) / i]
• Nominal vs effective interest rate conversions
• Simple interest A = P(1 + in) and linear depreciation A = P(1 − in)
• Effective rate: 1 + i_eff = (1 + i_nom/m)ᵐ
• Outstanding balance of a loan after some payments
• Using logarithms to solve for n

Worked examples

R5 000 invested at 8% p.a. compounded monthly for 5 years.

i = 0.08/12, n = 60. A = 5000(1 + 0.08/12)⁶⁰ ≈ R7 449.23.

Convert 12% p.a. compounded monthly to an effective annual rate.

1 + i_eff = (1 + 0.12/12)¹² = 1.01¹² ≈ 1.126825, so the effective rate is about 12.68% p.a.

A car worth R250 000 depreciates at 15% p.a. on the reducing balance. What is it worth after 4 years?

A = 250 000(1 − 0.15)⁴ = 250 000 × 0.85⁴ ≈ R130 501.56.

Find the monthly repayment on a R1 200 000 home loan at 10.5% p.a. compounded monthly over 20 years.

i = 0.105/12 and n = 240. Use P = x[1 − (1 + i)⁻ⁿ] / i and solve for x: x = 1 200 000 × i / [1 − (1 + i)⁻²⁴⁰] ≈ R11 980.56 per month.

How long does it take R10 000 to double at 9% p.a. compounded annually?

2 = 1.09ⁿ, so n = log 2 / log 1.09 ≈ 8.04. The money has not quite doubled after 8 years; it has doubled once the 9th year's interest is added.

Common mistakes

• Using annual i and n when interest compounds monthly.
• Mixing up future value and present value annuity formulas.
• Off-by-one errors on n when the first payment is delayed.
• Rounding i to a few decimal places before substituting: store it in the calculator.
• Using the future value formula for a loan, which is a present value problem.

Exam tips

• Write down i and n before substituting — most marks are lost on setup, not arithmetic.
• A loan is a present value annuity; saving towards a target amount is a future value annuity.
• To find n, rearrange to (1 + i)ⁿ = a number, use logarithms, then interpret the answer in context.

In past papers

• NSC Nov 2024 Paper 1 Q6 — loan repayment annuity

Frequently asked questions

Are the annuity formulas on the formula sheet?

Yes. Both future and present value annuity formulas are provided in the CAPS Mathematics formula sheet.

What is the difference between a nominal and an effective rate?

The nominal rate is the quoted annual rate that is compounded several times a year. The effective rate is the equivalent rate compounded once a year, so it shows the true annual growth.

How do I find the outstanding balance on a loan?

Find the present value of the payments still to be made. Alternatively, subtract the future value of the payments already made from the future value of the original loan amount at the same time.