Finance

Simple and compound interest

Hire-purchase, bank accounts, stokvels. Know which formula the document is using.

CAPS

Grade 11 · Mathematical Literacy · Finance

Mathematical Literacy uses a context, not a bare sum.

Two papers
Paper 1 uses familiar contexts: pay slips, till slips, maps you have seen, and data in a table. Paper 2 uses less familiar contexts and expects you to decide which method fits. Both papers are 150 marks.
What to show
Write the value with its unit or its rand sign. Say whether you multiply or divide, and round only at the end, in the way the question asked (nearest rand, one decimal place, a whole number of tiles).
The relation
A = P(1 + in) A = P(1 + i)ⁿ. Simple interest vs compound interest
How a marker reads it
i is 0.10, not 10. n is in years. If interest is monthly, convert n to years or i to a monthly rate — match the paper.

A correct number with the wrong unit, or a VAT amount treated as the full price, loses the mark the context was testing.

Diagram

Worked example

R2 000 at 10% p.a. simple interest for 3 years. Amount?

Before any working — hunt first

Given

Numbers and units already in the sentence: R2 · 000 at · 10% · 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: Amount. Circle that word — that is the missing variable.

Find

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

Calculate

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

Simplified approach

Simple: interest = P × i × n, then add to P. Or A = P(1+in).

Culture note

A furniture hire-purchase in a Polokwane mall is usually simple interest unless they say compounded.

Formulas

A=P(1 + in)A=P(1 + i)ⁿ

Simple interest vs compound interest

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.

If the price already includes VAT, divide by 1.15 — do not subtract 15%
How:Total = price × 1.15 when VAT is still to be added. When the till already shows VAT, price excluding = total1.15. Subtracting 15% of the total is a different number and loses the mark.
When to use it:Till slips, VAT, and SARS-style tax questions.
Fencing is perimeter. Grass, paint and tiles are area. Tanks are volume.
How:Underline the object: wire, border, fence → add the sides. Floor, wall, field, paint → multiply length by width, then divide by coverage and round tins up. Water in a tank → m³ then × 1 000 for litres.
When to use it:Measurement papers: school fields, paint, Jojo tanks.
Always substitute the usage into both tariff options — the cheaper one can swap after break-even
How:Write cost A and cost B as two lines. Set them equal if they ask where the deals match. Circle the smaller total at the given usage. A graph with two lines makes the swap obvious.
When to use it:Cellphone contracts, prepaid electricity, and cake-sale break-even.

Step 1 / 5

Identify simple

The paper says simple interest. Use A = P(1+in), not the compound formula.

Simple interest and compound interest — Diagram

A=2000(1 + 0.10×3)=2000×1.3=2600

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.

4. Step-by-step working

01
Identify simple
The paper says simple interest. Use A = P(1+in), not the compound formula.
A=2000(1 + 0.10×3)=2000×1.3=2600
02
Substitute with i as a decimal
Amount = R2 600. Interest earned is R600.

More worked examples

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

Example 1 / 20

R5 000 is invested at 8% per year simple interest for 3 years. Calculate the interest and the final amount.

4. Step-by-step working

01
Write the formula
Simple interest stays on the original amount. I = P × r × t.
I=Prt
02
Multiply
8% of R5 000 is 0.08 × 5 000 = R400 in one year.
0.08×5 000=400
03
Multiply
Three years: 400×3=R1 200.
400×3=1 200
04
Add
Final amount=5 000+1 200=R6 200.
5 000+1 200=6 200

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: R5 000 is invested at 8% per year simple interest for 3 years. Calculate the interest and the final amount.

Before any working — hunt first

Given

Numbers and units already in the sentence: R5 · 000 is · 8% · 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: the interest and the final amount. Circle that word — that is the missing variable.

Find

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

Calculate

Write I = Prt with empty letters. Cross out every letter that already has a number. Calculate the letter that is still standing — that gives the interest and the final amount.

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

If you have never seen this before: Simple interest is I = Prt, calculated on the original amount every year. The final amount is P + I. 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 = R5 000, r = 8% = 0.08, t = 3 years. Simple interest, not compound.

3. Which method — and why this one?

Simple interest is I = Prt, calculated on the original amount every year. The final amount is P + I.

4. Step-by-step working

01 / 07
Write the formula
Simple interest stays on the original amount. I = P × r × t.
I=Prt
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 / 07
Multiply
8% of R5 000 is 0.08 × 5 000 = R400 in one year.
0.08×5 000=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 / 07
Multiply
Three years: 400×3=R1 200.
400×3=1 200
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.
04 / 07
Add
Final amount=5 000+1 200=R6 200.
5 000+1 200=6 200
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.
05 / 07
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.
06 / 07
Step F — Box the answer with its unit
Interest R1 200. Amount R6 200.
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.
07 / 07
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

Interest R1 200. Amount R6 200.

Copy onto your answer sheet — in this order

Formula: I=Prt

Answer: Interest R1 200. Amount R6 200.

6. Check it like a marker

A = P(1 + i)ⁿ is compound interest. It would give R6 298.56 here, and the question did not say compounded.

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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