HomeTopicsFinance & Growth

Finance & Growth

Grade 10 CAPS: simple and compound growth, hire purchase, inflation, population growth, and the impact of a changing exchange rate. Includes real DBE and provincial exam questions.

Grade 10Grade 11Grade 12
1. Guided Course 2. Mastery Bank 3. Quick Test
CAPS alignedGrade 10Paper 1Interactive notes
Guided Course Slides
Quick checks: 0/0
Grade 10 CAPS Mathematics

Finance & Growth

From simple interest to compound interest; from hire purchase to inflation; from population growth to the Rand in your pocket on an overseas trip. Work through the slides in order, then move to the practice bank.

Scope check:Official CAPS requirement

Your 3.5-hour learning route

One idea building on the next: growth, then four real-world uses of it.

45
min
1. Simple vs compound

The one distinction every later slide depends on.

40
min
2. Hire purchase

Deposit, then simple interest on what's left.

35
min
3. Inflation

Compound growth applied to prices, forward and backward.

35
min
4. Population growth

The same formula, a different real-world quantity.

35
min
5. Foreign exchange

Why a weaker Rand changes what things really cost.

Study rule
Before touching any formula, decide: does this grow by the same RAND amount every year, or the same PERCENTAGE of an already-grown amount? That answer alone tells you simple or compound.

What CAPS actually asks in Grade 10

One real-world topic, applied to five different everyday contexts.

  • 1

    Use the simple and compound growth formulae to solve problems, including annual interest, hire purchase, inflation, population growth and other real-life problems.

  • 2

    Understand the implication of fluctuating foreign exchange rates — for example on the petrol price, imports, exports, and overseas travel.

Not yet
Depreciation, decay formulae, and nominal vs effective interest rates are Grade 11 content — this page is Grade 10 growth only.

Simple growth vs compound growth

The single distinction every other slide on this page depends on.

Simple growth
\[A=P(1+in)\]

Interest is calculated on the ORIGINAL amount only, every period. The interest earned never itself earns interest.

Compound growth
\[A=P(1+i)^n\]

Interest is calculated on the PREVIOUS period's total. Interest earns interest — this is why \(n\) is an exponent, not a multiplier.

Worked example: comparing the two formulas

Same principal, same rate — watch them diverge.

R4 000 over 3 years Level 1–2

R4 000 is invested at 6% p.a. Compare the value after 3 years under simple interest and under compound interest.

Show both calculations
  1. 1Simple: \(A=4\,000(1+0{,}06\times3)=4\,000(1{,}18)=\boxed{R4\,720{,}00}\)
  2. 2Compound: \(A=4\,000(1{,}06)^3=\boxed{R4\,764{,}06}\)
  3. 3Both give identical growth after year 1 — they only start to diverge from year 2 onward.

Why the gap grows over time

A straight line vs a curve that bends upward.

R8 000 invested at 8% p.a. for 10 years: R14 400 under simple growth vs R17 271 under compound growth. The gap barely shows in year 1 or 2 — but it compounds, literally, the longer the money is invested.

Worked example: a dramatic long-term gap

Start with a shorter period, then take the same idea out to 15 years.

R5 000 over 5 years Level 1–2

R5 000 is invested for 5 years at 10% p.a. Calculate how much MORE the compound-interest investment is worth than the simple-interest investment.

Show the working
  1. 1Simple: \(5\,000(1+0{,}10\times5)=\boxed{R7\,500{,}00}\)
  2. 2Compound: \(5\,000(1{,}10)^{5}\approx\boxed{R8\,052{,}55}\)
  3. 3Difference: \(8\,052{,}55-7\,500{,}00=\boxed{R552{,}55}\) more, over 5 years.
R5 000 over 15 years Level 3–4

R5 000 is invested for 15 years at 10% p.a. Calculate how much MORE the compound-interest investment is worth than the simple-interest investment.

Show the complete working
  1. 1Simple: \(5\,000(1+0{,}10\times15)=\boxed{R12\,500{,}00}\)
  2. 2Compound: \(5\,000(1{,}10)^{15}\approx\boxed{R20\,886{,}24}\)
  3. 3Difference: \(20\,886{,}24-12\,500{,}00=\boxed{R8\,386{,}24}\) — almost 70% more, from the same starting amount and rate.
See the pattern
Same principal, same rate — but the gap grows from R552,55 at 5 years to R8 386,24 at 15 years. The longer the money is invested, the more compounding pulls ahead.

Hire purchase: deposit, then simple interest

A three-step method that never changes.

1
Deposit

Subtract it from the cash price first.

2
Interest

Simple interest, on the balance only.

3
Instalment

(Balance + interest) ÷ number of months.

Always true
Hire purchase interest is ALWAYS simple interest, and it is ALWAYS calculated on the balance after the deposit — never compound, and never on the full cash price.

Worked example: hire purchase with a real complication

First the plain three-step method, then a genuine DBE exam question with a fee the formula alone won't catch.

A basic hire purchase agreement Level 2

An item priced at R6 000 is bought on hire purchase: a 20% deposit, with the balance repaid at 15% p.a. simple interest over 24 months. Calculate the monthly instalment.

Show the working
  1. 1Deposit \(=0{,}20\times6\,000=R1\,200\); balance \(=R4\,800\)
  2. 2Interest \(=4\,800\times0{,}15\times2=R1\,440\)
  3. 3Total \(=4\,800+1\,440=R6\,240\), over 24 months: \(\boxed{R260{,}00}\) per month
A dishwasher, on hire purchase Level 4

Sylvia wants to buy a dishwasher priced at R9 899 by means of a hire purchase agreement: a 30% deposit; 12% p.a. simple interest on the balance; a compulsory monthly insurance premium of R65,30; the account settled over 36 months. Calculate her monthly instalment.

Show the complete exam working
  1. 1Deposit \(=0{,}30\times9\,899=R2\,969{,}70\); balance \(=R6\,929{,}30\)
  2. 2Interest \(=6\,929{,}30\times0{,}12\times3=R2\,494{,}55\)
  3. 3Total \(=6\,929{,}30+2\,494{,}55=R9\,423{,}85\), over 36 months \(=R261{,}77\)
  4. 4PLUS the compulsory R65,30 monthly insurance: \(261{,}77+65{,}30=\boxed{R327{,}07}\)
Real exam question:Eastern Cape DBE, Paper 1, November 2020 (Q4.1) — independently re-derived and confirmed to match the official memo.
Read every condition
A compulsory extra fee (like insurance) is added AFTER the loan instalment is calculated — it is never part of the interest calculation itself.
Quick check: growth & hire purchase

An amount grows so that every year's interest is calculated on the PREVIOUS year's total. Which formula models this?

In a hire purchase agreement, interest is charged on:

Inflation: compound growth applied to prices

The same formula — this time the "amount" is a price, not an investment.

Prices compound too
\[A=P(1+i)^n\]

\(P\) is today's price, \(i\) is the inflation rate, \(n\) is the number of years, and \(A\) is the future price. This works BACKWARD too: if \(A\) is known, divide to find \(P\).

Worked example: inflation, forward and backward

A genuine DBE exam question solved in reverse.

Projecting a future price Level 2

An item currently costs R450. If inflation is 5,5% p.a., calculate its expected price in 3 years' time.

Show the working
\(A=450(1{,}055)^3=\boxed{R528{,}41}\)
Solving for the inflation rate Level 3

A cell phone has a cash price of R29 730,34 today. Due to inflation, its cash price is expected to rise to R31 968,11 after 3 years. Calculate the annual inflation rate.

Show the complete exam working
  1. 1\(31\,968{,}11=29\,730{,}34(1+i)^3\)
  2. 2\(1+i=\left(\dfrac{31\,968{,}11}{29\,730{,}34}\right)^{\frac13}\)
  3. 3\(\boxed{i\approx2{,}45\%}\)
Real exam question:KwaZulu-Natal Provincial Common Test, Grade 10, September 2024 (Q1.3) — independently re-derived and confirmed to match the official memo.

Population growth: the same formula, a new context

People, animals, bacteria — anything that grows by a constant percentage.

Compound growth, not people-specific

Population growth is ALWAYS compound growth: this year's growth is a percentage of an already-larger population than last year's. The formula \(A=P(1+i)^n\) works exactly as it does for money.

Worked example: a real population projection

A genuine DBE exam question.

Hartbeesfontein's population Level 2

The population of Hartbeesfontein is 4 831 people in 2023. Calculate the expected population over the next 10 years, based on an annual growth rate of 1,3%.

Show the working
\(A=4\,831(1{,}013)^{10}\approx\boxed{5\,497}\) people
Real exam question:North West DBE, Paper 1, November 2023 (Q4.1) — independently re-derived and confirmed to match the official memo.

Worked example: comparing two growing populations

First read two populations off a fixed year, then find the year a slower town overtakes a faster-starting one.

Which town is bigger after 5 years? Level 2

Town C has a population of 20 000, growing at 5% p.a. Town D has a population of 25 000, growing at 3% p.a. Calculate each town's population after 5 years, and state which is bigger.

Show the working
  1. 1Town C: \(20\,000(1{,}05)^5\approx\boxed{25\,525{,}63}\)
  2. 2Town D: \(25\,000(1{,}03)^5\approx\boxed{28\,981{,}85}\)
  3. 3\(\boxed{\text{Town D is still bigger}}\) after 5 years, even though it grows more slowly — its head start hasn't been overtaken yet.
Two towns, two rates Level 4

Town A has a population of 50 000, growing at 3,2% p.a. Town B has a population of 38 000, growing at 4,5% p.a. After how many complete years will Town B's population first exceed Town A's?

Show the complete working
  1. 1Solving \(38\,000(1{,}045)^n>50\,000(1{,}032)^n\) gives a raw \(n\approx21{,}92\).
  2. 2At \(n=21\): Town A \(\approx96\,882\), still ahead of Town B \(\approx95\,769\).
  3. 3At \(n=22\): Town B \(\approx100\,079\) has overtaken Town A \(\approx99\,982\).
  4. 4\(\boxed{22\text{ years}}\) — never leave the raw, unrounded value as your final answer.
Quick check: inflation & population

A price today is the future value of the price 3 years ago. To find the price 3 years ago, you should:

A raw calculation gives n = 6,3 years for a population to reach a target. What should your final answer be?

Foreign exchange: why the rate matters

The same trip, the same car, the same trade — a different Rand cost.

A weaker Rand costs you more

If R1 buys fewer US dollars (the Rand "weakens"), then it takes MORE Rand to buy the same imported item, book the same overseas trip, or pay for the same foreign holiday. Exporters, by contrast, benefit from a weaker Rand.

Real-life impact
CAPS specifically names the petrol price, imports, exports, and overseas travel as examples where a fluctuating exchange rate has a direct, real impact on your life.

Worked example: comparing a price in two currencies

A genuine DBE exam question — you cannot compare raw numbers in different currencies.

Which country is cheaper? Level 4

George, from England, sees a machine for $6 800 in the USA. A similar machine costs £4 600 in England. Given $1=R16,24 and £1=R27,63, in which country is the machine cheaper for George to buy?

Show the complete exam working
  1. 1Convert the USA price to Rand: \(6\,800\times16{,}24=R110\,432{,}00\)
  2. 2Convert that to Pounds: \(R110\,432{,}00\div27{,}63\approx£3\,996{,}82\)
  3. 3Since \(£3\,996{,}82<£4\,600\), \(\boxed{\text{the machine is cheaper in the USA}}\)
Real exam question:Eastern Cape DBE, Paper 1, November 2020 (Q4.2) — independently re-derived and confirmed to match the official memo.

Worked example: the cost of a changing exchange rate

The same trip can genuinely cost more if you wait to pay for it.

A trip that got more expensive Level 3

An overseas trip costs $1 200. When it was booked, the exchange rate was R17,20 to $1. By the time it is paid for, the rate has changed to R18,60 to $1. Calculate how much MORE, in Rand, the trip now costs.

Show the working
  1. 1Original cost: \(1\,200\times17{,}20=R20\,640{,}00\)
  2. 2New cost: \(1\,200\times18{,}60=R22\,320{,}00\)
  3. 3\(\boxed{R1\,680{,}00}\) more — the Rand weakened, so the same $1\,200 now needs more Rand to buy.
Quick check: foreign exchange

The Rand weakens against the US Dollar (more Rand is now needed to buy $1). What happens to the Rand cost of an imported item priced in Dollars?

To compare a price in Dollars with a price in Pounds, you should first:

Mistake clinic: repair the exact error

Small slips that break an otherwise correct answer.

Formula choice

Simple ≠ compound

"Every year, on the original amount" is simple. "On the previous total" is compound. Read the wording carefully every time.

Hire purchase

Never forget the deposit

Interest is only ever charged on the balance AFTER the deposit is subtracted.

Direction

Forward or backward?

Decide which value is "in the future" before choosing to multiply or divide by \((1+i)^n\).

Rounding

Check both boundary years

A raw decimal value for "number of years" is never a final answer — test the year below and above it directly.

Currency

Convert before comparing

Two prices in two different currencies can never be compared until both are in the same currency.

Your Paper 1 checklist

Use this before submitting an exam answer.

Avoid this

Confusing simple and compound growth.

Forgetting the hire purchase deposit.

Leaving a raw decimal as a final year count.

Do this

Ask "original amount, or previous total?" first.

Subtract the deposit before calculating interest.

Check both boundary years for any "number of years" question.

Apply both simple and compound growth formulas correctly.
Calculate a full hire purchase instalment, including any extra fees.
Project a future price or population, and work backward to a past one.
Solve for an unknown rate or time period in a growth context.
Explain and calculate the impact of a changing foreign exchange rate.
More explanation and exercises:Siyavula Grade 10 Finance and Growth
Summary complete

You now have the route.

Use the Mastery Bank to build fluency. Then take the test without notes and use the result to choose the exact slide to revisit.

Next step 1

Mastery Bank

17 questions, including 5 real DBE exam questions, from a direct growth calculation through to comparing two currencies. Answers reveal only after your attempt.

Next step 2

Quick Test

A short exam-style self-check. Mark it, then revisit the exact slide that matches a missed skill.

1 / 23

Learn It in Short Videos

Four free, independent videos — not made by Equation Station SA.

Hire Purchase: Introduction

The deposit-then-simple-interest method, worked step by step.

Kevinmathscience · Financial Maths Grade 10, Hire Purchase Introduction

Compound Interest: Introduction

Why compound growth pulls ahead of simple growth over time.

McClatchey Maths · Compound Interest: Part 1 Introduction

Intro to Inflation

Why prices compound over time, exactly like an investment.

MishDoesMath · Grade 10 Math: Intro to Inflation

Population Growth

Projecting a population forward using the compound growth formula.

MishDoesMath · Grade 10 Math: Population growth

Practise in the right order

The core teaching is above. These are the next steps, not a replacement for it.

01
Built-in practice
Finance & Growth Mastery Bank

17 questions by skill, including 5 real DBE/provincial exam questions, with concise reveal answers.

Start after the slides
Open Mastery Bank
02
Built-in check
Test Your Knowledge

Use the short exam-style self-check when you want a fast confidence check.

Then target one weak skill
Take the Quick Test
CAPS
Free textbook chapter
Siyavula: Grade 10 Finance

Use its own worked examples for extra explanation and exercises.

Free • CAPS aligned
Open Siyavula
DBE
Official free books
DBE Grade 10 Textbooks

Official state-owned learner books and teacher support for Grade 10 Mathematics.

Official • free access
Open DBE Books
PDF
Printable worksheet
Maths At Sharp: Grade 10 Finance

A free CAPS chapter on simple and compound growth, hire purchase, inflation and exchange rates, with fully worked solutions.

Free • download & print
Open Worksheet
x

Related Topics

This topic continues into Grade 11 and Grade 12.

%

Finance & Growth (Grade 11)

Decay, depreciation, effective rates

Study this →
%

Finance, Growth & Decay (Grade 12)

Annuities, loans, critical analysis

Study this →
x

Algebra (Grade 10)

Exponents and equations

Study this →
Student Questions

Frequently Asked Questions

Short answers for the checks learners make while preparing for the Grade 10 CAPS exam.

What does CAPS require for Grade 10 Finance and Growth?

Use the simple and compound growth formulae to solve problems including annual interest, hire purchase, inflation, population growth and other real-life problems, and understand the implication of fluctuating foreign exchange rates.

What is the difference between simple and compound growth?

Simple growth calculates interest on the original amount only, every period. Compound growth calculates interest on the previous period's total, so interest itself earns interest.

Is depreciation part of Grade 10 Finance?

No. Straight-line and reducing-balance depreciation, decay formulae, and nominal versus effective interest rates are Grade 11 content.

Where should I practise next?

Finish the interactive slides, open the Mastery Bank, then take the short self-test without notes.