Financial Maths: Interest, Hire Purchase & Exchange Rates

Simple and compound interest, hire purchase, rentals, exchange rates and commission — the real-world money maths of Grade 9, taught with the formulas, fully worked examples and a quiz.

This is the topic you will use for the rest of your life. Every loan, savings account, cellphone contract and shop "lay-by" runs on the maths below — and it is examined every single year.

1Simple interest

Simple interest grows in a straight line; compound interest curves upward as interest earns interest.

With simple interest the interest is worked out on the original amount every year, so you earn (or pay) the same amount annually.

SI = P × r × n100
P = principal (starting amount) · r = rate % · n = number of years

Worked ExampleR8 000 is invested at 12% simple interest per annum for 2 years

1
Write the formula: SI = (P × r × n) ÷ 100.
Always start by writing the formula — it earns a mark.
2
SI = (8 000 × 12 × 2) ÷ 100.
Substitute P = 8000, r = 12, n = 2.
3
SI = 192 000 ÷ 100 = R1 920.
That is the interest only.
4
Total amount = 8 000 + 1 920 = R9 920.
The question usually wants the final amount too.

2Compound interest

With compound interest the interest is added to the amount, and the next year's interest is worked out on that bigger amount. Interest earns interest — which is why savings grow faster and debt gets dangerous.

A = P(1 + r100)ⁿ

Worked ExampleR5 000 is invested at 10% compound interest for 3 years

1
A = 5 000(1 + 10100)³.
Substitute into the formula.
2
= 5 000(1,1)³.
1 + 0,1 = 1,1.
3
= 5 000 × 1,331 = R6 655.
Work out the power first, then multiply.
4
Interest earned = 6 655 − 5 000 = R1 655.
Simple interest would have given only R1 500 — compound is more.

💡

Read the question carefully for the word "compound" or "simple". Using the wrong formula loses every mark in the question.

3Hire purchase

Hire purchase (HP) means buying on instalments. You usually pay a deposit, then monthly payments that include simple interest on the balance.

Worked ExampleA fridge costs R6 000. Pay 10% deposit, then 24 monthly instalments at 15% p.a. simple interest

1
Deposit = 10% of 6 000 = R600.
2
Balance owed = 6 000 − 600 = R5 400.
Interest is charged on this balance.
3
Interest = (5 400 × 15 × 2) ÷ 100 = R1 620.
24 months = 2 years.
4
Total to repay = 5 400 + 1 620 = R7 020, so each instalment = 7 020 ÷ 24 = R292,50.
Divide by the number of months.

4Exchange rates

Worked ExampleIf £1 = R23,50, how many rands is £40?

1
Multiply: 40 × 23,50.
Going from pounds TO rands, multiply by the rate.
2
= R940.
3
Going the other way (rands to pounds) you would divide by 23,50.
Always check which direction the question asks.

5Commission and rentals

Worked ExampleA salesperson earns 8% commission on sales of R45 000

1
Commission = 8% of 45 000.
"Of" means multiply.
2
= 0,08 × 45 000 = R3 600.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
Find the simple interest on R4 000 at 9% p.a. for 3 years.
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(4000×9×3)÷100 = R1 080
2
R2 500 at 7% simple interest for 4 years — what is the total amount?
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SI = R700 → total = R3 200
3
Find the amount when R10 000 is invested at 5% compound interest for 2 years.
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10000(1,05)² = R11 025
4
R6 000 at 10% compound interest for 3 years — total amount?
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6000(1,1)³ = R7 986
5
A TV costs R9 000. A 15% deposit is paid. How much is the deposit?
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0,15 × 9000 = R1 350
6
Using that deposit, what balance is owed?
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9000 − 1350 = R7 650
7
If $1 = R18,20, convert $150 to rands.
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150 × 18,20 = R2 730
8
If $1 = R18,20, convert R910 to dollars.
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910 ÷ 18,20 = $50
9
Calculate 6% commission on sales of R80 000.
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0,06 × 80000 = R4 800