Compound Interest and Depreciation

Active learning turns abstract repeated percentage changes into concrete experiences. Students manipulate multipliers, compare timelines, and debate outcomes, which builds durable understanding beyond textbook formulas.

• Year 11
• Mathematics
• 4 activities
• 30 min–50 min

Learning Objectives

1. Calculate the future value of an investment with compound interest over specified periods using multipliers.
2. Determine the depreciated value of an asset after a set number of years using depreciation multipliers.
3. Compare the financial outcomes of simple interest versus compound interest over extended timeframes.
4. Explain the mathematical reasoning behind using multipliers for repeated percentage changes.
5. Analyze the long-term impact of varying interest rates or depreciation percentages on financial scenarios.

Ready-to-Use Activities

Decision Matrix

⏱ 45 min·Small Groups

Savings Simulator: Group Challenges

Provide groups with calculators and scenario cards detailing initial amounts, rates, and periods. Students apply multipliers step-by-step to compute compound interest, then graph results. Groups present one key insight, such as doubling time at different rates.

Prepare & details

Compare compound interest to simple interest over extended periods.

Facilitation Tip: During Savings Simulator, circulate with colored tokens to physically show how each group’s pile grows faster than the last when compound interest is applied.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 30 min·Pairs

Depreciation Relay: Pairs Race

Pairs receive asset cards with starting values and annual depreciation multipliers. One student calculates one period, passes to partner for the next, racing against other pairs to 10 years. Debrief compares straight-line versus compound models.

Prepare & details

Explain why a multiplier is an efficient tool for calculating percentage changes.

Facilitation Tip: For Depreciation Relay, station a timer at each card set so pairs race against the clock while ensuring they use the multiplier under one each round.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 35 min·Whole Class

Multiplier Match-Up: Whole Class

Distribute cards with percentage changes, multipliers, and scenarios. Students match them in a class mingle, then verify calculations on boards. Discuss efficiencies of multipliers over repeated division/multiplication.

Prepare & details

Analyze the long-term financial implications of different interest rates or depreciation values.

Facilitation Tip: In Multiplier Match-Up, give every student a card with a starting value and percentage change so the whole class can simultaneously pair multipliers to scene cards on the board.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Decision Matrix

⏱ 50 min·Small Groups

Investment Debate: Small Groups Prep

Assign groups simple versus compound interest scenarios over 20 years. They calculate outcomes, prepare arguments for best choice, and debate. Vote on most convincing evidence with supporting maths.

Prepare & details

Compare compound interest to simple interest over extended periods.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Teaching This Topic

Teach multipliers as a mathematical shortcut first, then anchor them in real contexts. Avoid rushing to the formula—let students derive the power rule by chaining small multipliers over several rounds. Research shows concrete–abstract–abstract sequences work best for percentage change, so move from physical tokens to tables to pure multipliers.

What to Expect

Success looks like students confidently selecting the correct multiplier, explaining why compound interest outpaces simple interest over time, and using decreasing multipliers correctly for depreciation scenarios.

Watch Out for These Misconceptions

Common Misconception

During Savings Simulator, watch for students who keep adding the same percentage of the original amount instead of the new total.

What to Teach Instead

Have peers in each group rebuild their token pile using the new total after each round and compare the growth curve to a simple interest timeline laid beside it.

Common Misconception

During Depreciation Relay, watch for students who subtract a fixed amount each year rather than applying a decreasing multiplier.

What to Teach Instead

Pause the relay and ask each pair to sort their asset value cards in descending order, then ask them to explain why the gaps between cards shrink over time when using the correct multiplier.

Common Misconception

During Multiplier Match-Up, watch for students who think multipliers can only be used for one period and resist raising them to a power.

What to Teach Instead

Ask students to chain three identical multipliers on a mini-whiteboard and then prompt them to write the single equivalent multiplier as a power, verifying with calculators.

Assessment Ideas

Quick Check

After Savings Simulator, give each group a new mini-scenario on a card. Ask them to show their multiplier calculation and final balance on a mini-whiteboard within two minutes while you circulate to check for correct exponentiation.

Discussion Prompt

During Investment Debate prep, listen for students who correctly justify compound interest’s long-term advantage and note whether they reference repeated multiplication versus fixed additions.

Exit Ticket

Conclude Multiplier Match-Up by giving each student a different depreciation scenario. Ask them to calculate the value after 4 years using the correct multiplier and write one sentence explaining why the multiplier method is efficient for repeated percentage decreases.

Extensions & Scaffolding

• Challenge early finishers to find the exact interest rate that would make a £1000 investment double in 10 years using trial and error with different multipliers.
• Scaffolding for struggling students: provide a partially completed table with one multiplier already filled in to reduce cognitive load.
• Deeper exploration: invite students to research how banks or lenders actually quote APR versus AER and calculate the real difference for a £5000 loan over 5 years.

Key Vocabulary

Compound Interest	Interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.
Depreciation	The decrease in value of an asset over time, often due to wear and tear, age, or obsolescence.
Multiplier	A number used to multiply another number; in this context, it represents a percentage increase (greater than 1) or decrease (less than 1) applied repeatedly.
Principal	The original amount of money invested or borrowed, before any interest or fees are applied.