Key Stage: KS3
Year group: Year 9
Age range: 13–14
Duration: 55 minutes
Subject: Maths / PSHE / Citizenship
Cost: Free

Learning aim

Pupils can calculate compound interest using the formula A = P(1 + r/100)^n and explain why starting to save early matters more than the interest rate.

CURRICULUM National Curriculum links

Maths KS3: "solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics"
Maths KS3: use exponential equations to solve compound interest problems
PSHE Association KS3 L25: about different ways to save money
Citizenship KS3: managing personal finances

RESOURCES What you'll need

Compound interest worksheet (with formula)
Two saver scenarios printed: "Sarah saves at 18" vs "Tom saves at 30"
Graph paper (1 sheet per pupil)
Calculators (mandatory)

LESSON Lesson structure (55 minutes)

Opening
HOOK

Pose this classic: "Would you rather have £1 a day for 30 days, OR 1p doubled every day for 30 days?" Take votes. Most pick £1/day = £30 total. Reveal: doubling 1p for 30 days = £5,368,709.12 (over five million pounds). That's what compounding does. Compound interest works the same way — just slower.

Direct teach
TEACH

Define and contrast: Simple interest = interest only on the original deposit; Compound interest = interest on the original PLUS interest already earned. Show the formula: A = P × (1 + r/100)ⁿ, where A = final amount, P = principal (starting amount), r = rate (%), n = number of years. Worked example on the board: £100 at 5% for 10 years = £100 × 1.05¹⁰ = £162.89. Same money at simple interest = £150. Difference: £12.89 — and it grows each year.

Pupils apply
GUIDED

Pupils calculate compound interest for £1,000 at 5% over 5, 10, 20, and 30 years using their calculators. Record on the worksheet. Then plot the results on graph paper: years on x-axis, amount on y-axis. They'll see the curve — slow at first, then accelerating. Discuss: when does the growth really take off? (Years 20+.)

Stretch / depth
CHALLENGE

The most important real-world scenario: "Sarah starts saving £100/month at age 18 and STOPS at age 28 (10 years of saving, then nothing more). Tom starts saving £100/month at age 30 and saves until 65 (35 years of saving). Both earn 7% average return per year. Who has more at age 65?" Pupils calculate. Reveal: Sarah's earlier 10 years of saving (£12,000 in total) BEATS Tom's 35 years (£42,000 in total). Sarah ≈ £200,000 at 65, Tom ≈ £170,000. Build the insight: starting early matters more than saving longer.

Close
PLENARY

Each pupil uses the formula to write a prediction: "If I started saving £20/month at age 18 at 5% interest, by age 60 I would have approximately ___." Share three answers. Final reflection: "Why don't more people start saving at 18?"

DIFFERENTIATION Adapting for all learners

Support (working below ARE)

Use round numbers (£100 starting at 10% for 5 years) and a calculator throughout. Provide a worked example to copy. Focus on understanding the curve shape rather than calculation precision.

Stretch (working above ARE)

Pupils derive the formula themselves from first principles. Calculate a 50-year compound. Then: "What happens if the interest rate is 0%? Negative?" Discuss real-world cases (savings accounts paying below inflation = real loss).

SEND SEND adaptations

For pupils with dyscalculia: pre-fill the table with the calculator results, pupils identify the pattern visually. For pupils with autism: provide the formula as a step-by-step "recipe" — fill in each variable in order. For visually impaired pupils: use audio-described graph examples.

EAL EAL support

Vocabulary: "interest", "compound", "principal", "rate", "annual", "deposit", "exponential". Sentence frame: "After ___ years, my £___ at ___% interest becomes £___."

ASSESSMENT Assessment criteria

Pupils can: (1) calculate compound interest on £100 at 5% for 10 years using the formula; (2) explain in their own words why compound interest grows faster than simple interest; (3) identify why starting to save early matters more than the interest rate; (4) plot a compound-interest curve.

HOME Homework pack

Four activities to deepen understanding of compound interest. ~30 minutes.

Calculate it

What pupils do: Work out the value of £100 after 5 years at 4% per year compound interest. Show your working (multiply by 1.04 five times, or use 100 × 1.04⁵).

Expected output: Step-by-step calculation showing each year's ending balance.

Marking guidance: 1 mark per year-end balance (5 marks), 1 mark for a correct final answer (~£121.67).

Simple vs compound

What pupils do: Compare £1,000 at 5% over 10 years using (a) simple interest and (b) compound interest. Show both totals. What is the difference?

Expected output: Two final totals plus the difference.

Marking guidance: 2 marks each for correct simple (£1,500) and compound (~£1,628.89), 2 marks for the difference.

The doubling time

What pupils do: Use the "Rule of 72" to find how long it takes money to double at: 4%, 6%, 8%, 12%. (Rule: 72 / rate = approximate years.)

Expected output: A 4-row table with rate and doubling time.

Marking guidance: 1 mark per accurate answer (18, 12, 9, 6 years). 4 marks total.

Extension (optional)

What pupils do: A teenager invests £50 a month from age 18 to 65 at 7% average return. Estimate the final value using an online compound interest calculator. Why is starting early so powerful?

Expected output: A final value plus a 3-sentence explanation.

Marking guidance: Up to 5 marks for accurate calculation and clear reasoning.

Family discussion prompt (safeguarding-aware)

Ask a grown-up: "Have you ever earned interest on savings? Did it grow faster or slower than you expected?"

SAFEGUARDING Classroom safeguarding

Note for teachers: Use fictional savers (Sarah, Tom) throughout. Do not ask pupils about their family's savings or whether they themselves have a savings account. Be aware some pupils may have no savings — frame the lesson as "what compound interest can do when you have money to save".

ANSWERS Answer key & differentiation

Answer guide

Guided table, £1,000 at 5%: 5 years £1,276.28; 10 years £1,628.89; 20 years £2,653.30; 30 years £4,321.94. The plotted curve visibly steepens beyond year 20.
Challenge: Sarah's £12,000 (ages 18–28, then left invested) ends around £200,000; Tom's £42,000 (ages 30–65) around £170,000 at 7% — the early start wins despite paying in £30,000 less.
Plenary (£20/month from 18 to 60 at 5%): roughly £33,000 from about £10,000 paid in — accept £30,000–£36,000 depending on whether pupils compound monthly or annually.
Homework: £100 at 4% for 5 years = £121.67 (year-ends £104.00, £108.16, £112.49, £116.99, £121.67); simple vs compound on £1,000 at 5% over 10 years = £1,500 vs £1,628.89, difference £128.89; Rule of 72 doubling times = 18, 12, 9 and 6 years; £50/month extension ≈ £200,000 (accept £180,000–£220,000).

Support (scaffold)

Replace the power with a chain: type 100 × 1.05, then keep pressing = (or use ANS × 1.05) once per year, recording each result.
Provide the guided table part-filled; pupils complete two cells and describe the pattern.
Estimate before calculating ("more or less than £150?") so wild calculator slips get caught.

Stretch (challenge)

Test the Rule of 72 against the exact formula at 6% — how close is 12 years, and why does the shortcut work?
Recompute £1,000 at 5% for 10 years compounding monthly (r/12, n × 12) and explain the small gain over annual.
Real vs nominal: if prices rise 2% a year while savings earn 5%, what is the real growth rate, and does the curve still steepen?

Saving for a goal — how long would it take? (KS2)
ISAs explained — the tax-free way to save (KS4 · Year 10)
First bank accounts at 11-15 — features and safe habits (KS3 · Year 7 / Year 9)
All lesson plans (KS1 · KS2 · KS3 · KS4) →