Finance

Simple & compound interest

A = P(1+in) and A = P(1+i)ⁿ.

CAPS

Grade 10 · Mathematics · Finance

This sits on Mathematics Paper 1.

The paper
Paper 1 is algebra, exponents, equations, number patterns, functions, finance and probability. Copy the formula, then substitute.
Cognitive level
CAPS spreads the marks across knowledge, routine procedures, complex procedures and problem solving. A routine question still wants the line of working. A problem-solving question wants you to choose the method, not only to calculate.
The relation
A = P(1 + in). Simple interest
How a marker reads it
Convert 9% to 0.09. Round money to two decimals.

Each Mathematics paper is 150 marks. A correct substitution can earn a method mark even when the last arithmetic slips, if the formula was the right one.

Diagram

Worked example

R8 000 at 9% p.a. compounded annually for 3 years. Accumulated amount?

Before any working — hunt first

Given

Numbers and units already in the sentence: R8 · 000 at · 9% · 3 years. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: Accumulated amount. Circle that word — that is the missing variable.

Find

We are required to find: Accumulated amount. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write A = P(1 + in) with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives Accumulated amount.

Simplified approach

Use A = P(1+i)ⁿ with i = 0.09, n = 3.

Culture note

A stokvel in Mamelodi that leaves the pot for three years is compound growth.

Formulas

A=P(1 + in)

Simple interest

A=P(1 + i)ⁿ

Compound interest

How to hunt the missing letter

Do not start by naming the letters. First hunt the missing one: copy every number you can see (Given). The letter with no number is Missing. The asking word is Find. The formula that still contains that letter is what you Calculate.

How to hunt: (1) Underline every number and its unit — those are Given. (2) Circle the asking word — find, calculate, how far, what is. That word names Find. (3) The letter the asking word names, which has no number yet, is Missing. (4) Write the formula with empty letters. Cross out every given letter. The letter still standing is what you Calculate.

P
principal
How you spot this in the sentence
When the sentence names the principal, that letter is P. Copy the number next to it into Given. If the sentence never names it, P is Missing. The starting amount you invest or borrow, in rands.
Example:If you invest R2 000, P = 2 000.
i
interest rate (decimal)
How you spot this in the sentence
When the sentence names the interest rate (decimal), that letter is i. Copy the number next to it into Given. If the sentence never names it, i is Missing. Write the percentage as a decimal: 8% → i = 0,08.
Example:12% per year means i=0,12.
n
number of periods
How you spot this in the sentence
When the sentence names the number of periods, that letter is n. Copy the number next to it into Given. If the sentence never names it, n is Missing. How many years (or compounding periods) the money sits.
Example:Five years→n=5.
A
accumulated amount
How you spot this in the sentence
When the sentence names the accumulated amount, that letter is A. Copy the number next to it into Given. If the sentence never names it, A is Missing. What the investment is worth at the end. A = P(1 + i)ⁿ for compound.
Example:P=1 000, i=0,1, n=2: A=1 000(1,1)²=R1 210.

Exam tricks you must know

These are the moves markers look for — not shortcuts that skip the method, but the habits that earn the method mark.

“Factorise fully” means HCF and then the identity — leaving 2(x² − 9) loses a mark
How:Look at the given polynomial. Pull out the biggest number and letter that divides every term (HCF). Then look at what is left: difference of squares, trinomial, or grouping. Both layers go on the page. Stop only when nothing else factorises.
When to use it:Any “factorise fully” on Paper 1, especially KZN.
Memorise exact values for 0°, 30°, 45°, 60°, 90° — compound angles collapse without them
How:Before a calculator, write the triangle: 30-60-90 and 45-45-90. sin 30° = 12, sin 45° = 1√2, sin 60° = √32, and the cosines swap. Compound-angle questions want these as fractions with division lines, not decimals.
When to use it:Reduction, compound angles, and “without a calculator” trig.
Name similar triangles in corresponding order: ΔABC ∼ ΔDEF, not ΔABC ∼ ΔEFD
How:Hunt equal angles first and mark them on the sketch. Then list vertices so that equal angles sit in the same position: A maps to D, B to E, C to F. The ratio statement uses that same order. Wrong order loses the reason mark even if the lengths are right.
When to use it:Similarity, intercept, and 3-D trig that shares a triangle.

Step 1 / 8

Step A — Read the question twice

Slow down. Circle the word that names the unknown. Underline every number and its unit. Do not grab a formula yet — first decide what the paper is actually asking.

Why this step: If you can say the method in a sentence, you will pick the right formula. First-timers skip this and grab the first equation they remember.

More worked examples

Board walkthroughs on this topic. Open one, copy the working, then try the next.

Example 1 / 20

Simple interest on R2000 at 10% p.a. for 2 years. Find I.

4. Step-by-step working

01
Write the formula
I=P i n.
I=Pin
02
Substitute
I=2000×0.1×2=R400.
I=400

How we got there

Read this like a teacher at the board. We go slowly, name every number, and say why we take each step.

Explain in another language · 11

1. What is the question asking?

Read the question twice. Circle the unknown. Underline every number and unit. The paper is asking: Simple interest on R2000 at 10% p.a. for 2 years. Find I.

Before any working — hunt first

Given

Numbers and units already in the sentence: R2000 at · 10% · 2 years. Copy each one into a column. A name without a number is not given.

Missing

After you copy the given, the letter that still has no number is missing. The paper is pointing at: I. Circle that word — that is the missing variable.

Find

We are required to find: I. Write that as a symbol on the left, with a question mark, before you touch a formula.

Calculate

Write I = Pin with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives I.

In other words — as if you have never seen this before

If you have never seen this before: I = Pin. Simple interest is a rectangle: principal × rate × time. We will name a method in words, write the formula with no numbers, then substitute one line at a time.

2. What do we already know?

P=2000, i=0.1, n=2. Unknown: I.

3. Which method — and why this one?

I = Pin. Simple interest is a rectangle: principal × rate × time.

4. Step-by-step working

01 / 05
Write the formula
I=P i n.
I=Pin
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
02 / 05
Substitute
I=2000×0.1×2=R400.
I=400
Why this step: We only do one job per line so a marker can follow the marks — and so you can find a slip without starting over.
03 / 05
Step G — Sense-check the size
Ask: is this the kind of number a Grade 10–12 paper would want? A speed of 3 000 ms for a learner walking, or a probability bigger than 1, means a unit or algebra slip. Estimate first: round the numbers and do the sum in your head.
Why this step: Markers write ‘unrealistic’ in the margin when the method is right but the size is wild. A 10-second head check often finds a missing 10² or a unit that never changed.
04 / 05
Step F — Box the answer with its unit
R400
Why this step: A number without a unit is half a mark on a Physics paper, and a marker can miss a Maths answer that is buried in working.
05 / 05
Step H — What the marker is looking for
On an NSC memo you usually earn: (1) a method mark for naming the right formula or idea in words, (2) an accuracy mark for substituting the given numbers with units, (3) an accuracy mark for the boxed answer with its unit. Write those three lines even if you are unsure of the arithmetic — blank pages score zero.
Why this step: First-timers chase the final number and leave the method blank. The memo still pays out for the idea and the substitution even when the last line is wrong.

5. The answer

R400

Copy onto your answer sheet — in this order

Formula: I=Pin

Answer: R400

6. Check it like a marker

Amount A=P+I=R2400.

7. A trap first-timers fall into

First-timers often grab the first formula they remember, mix units (cm with m, minutes with seconds), or drop a minus sign. Write the formula in words first: “this equals that, because…”

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