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Grade 12 Financial Maths Formulas

CAPS / NSC & IEB · Paper 1 · Annuities, loans & depreciation

R Growth & Decay

Simple interest $A = P(1 + in)$

Compound interest $A = P(1 + i)^{n}$

Straight-line depreciation $A = P(1 - in)$

Reducing balance $A = P(1 - i)^{n}$

Straight line takes the same rand amount off every year; reducing balance takes the same percentage off what is left, so it never reaches zero. "Book value" questions almost always mean reducing balance.

% Nominal & Effective Rates

Conversion $1 + i_{\text{eff}} = \left(1 + \dfrac{i^{(m)}}{m}\right)^{m}$

$i^{(m)}$ the nominal (quoted) annual rate

$m$ compounding periods per year

$i_{\text{eff}}$ the rate actually earned in a year

A quoted rate is nominal unless the question says "effective". You almost never need this formula to solve an annuity — divide the nominal rate by $m$ and count periods instead. It is for comparing two offers.

↑ Future Value — saving

Future value annuity $F = \dfrac{x\left[(1+i)^{n} - 1\right]}{i}$

$x$ the payment made each period

$n$ the number of payments, not the number of years

Used for sinking funds, retirement savings, "how much will I have"

This formula assumes the first payment is made at the end of the first period. If the question says payments start immediately, there is one extra payment period of growth — draw the timeline before deciding.

↓ Present Value — borrowing

Present value annuity $P = \dfrac{x\left[1 - (1+i)^{-n}\right]}{i}$

$P$ the amount borrowed today

$x$ the repayment each period

Used for home loans, car finance, "what can I afford"

Note the negative exponent — it is what makes this the present value. Writing $(1+i)^{n}$ here instead of $(1+i)^{-n}$ is the single most common slip in this section.

⊖ Outstanding Balance

After $k$ payments $P = \dfrac{x\left[1 - (1+i)^{-(n-k)}\right]}{i}$

The balance still owing is the present value of the payments still to come — so the only thing that changes is $n-k$ in the exponent. You do not need to know anything about the payments already made.

Total repaid $x \times n$

Total interest paid $(x \times n) - P$

? Which Formula Does the Question Want

The question says	Use	Because
One amount, left to grow	$A = P(1+i)^{n}$	a single deposit, no regular payments
Pays in each month, how much at the end	$F$ — future value	regular payments growing to a target
Borrows now, repays monthly	$P$ — present value	a lump sum today, paid off over time
How much is still owed	$P$ with $n-k$	the value of the payments still to come
Value of an asset after $n$ years	$A = P(1-i)^{n}$	depreciation on the reducing balance

Nearly every mark lost in financial maths is lost here, before any arithmetic happens. One question to ask: is there a payment every period, or only one amount? If there are regular payments it is an annuity; then the only remaining question is whether the money is being built up ($F$) or paid off ($P$).

⏱ Matching $i$ and $n$

Compounded	$i$ becomes	$n$ becomes
Annually	$i$	years
Half-yearly	$i \div 2$	years $\times\ 2$
Quarterly	$i \div 4$	years $\times\ 4$
Monthly	$i \div 12$	years $\times\ 12$

Divide the rate and multiply the periods by the same number, every time. $12\%$ per year compounded monthly is $i = 0{,}01$ and $n = 12$ per year — not $0{,}12$ and not $12$ years.

⚠ Where the Marks Actually Go

Counting payments $n$ is how many payments are made. A loan over 20 years paid monthly has $n = 240$, and "the last payment is in month 240" is a different statement from "20 years"

Deferred start if payments begin later than the first period, the annuity formula gives the value at the period before the first payment — grow it forward from there

Rounding early keep full accuracy in the calculator until the final line; a repayment rounded at an intermediate step is wrong by hundreds of rand over 240 months

The last payment it is usually smaller than the others, because the rounded repayment slightly overpays. If a question asks for it, it wants the outstanding balance

Draw the timeline. It takes fifteen seconds, it is worth method marks on its own, and it is the only reliable way to see whether a payment happens at the start or the end of a period.

Financial maths is lost in the first line, not the last.

The arithmetic is a calculator away; choosing between future and present value is where the marks go, and that is a teachable habit rather than a formula. I tutor Grade 12 maths one-to-one in Gqeberha, at your own table, in English or Afrikaans. The first consultation is free.

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An independent revision aid aligned to the CAPS/NSC Mathematics syllabus. Not an official Department of Basic Education document.