Understanding compound interest and depreciation is essential for both GCSE Maths success and real-life money management. These financial maths topics appear frequently in AQA, Edexcel, and OCR exam papers and provide students with practical numeracy skills that extend well beyond the classroom. In this guide, we will break down how compound interest and depreciation work, explain the underlying mathematical concepts, show how to apply the formulas step by step, and explore how to interpret exam-style questions with confidence.
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🔹 What Is Compound Interest?
Compound interest is the interest calculated on the initial amount (the principal) and any previously added interest. Unlike simple interest, which is calculated only on the original amount, compound interest takes into account the accumulated interest from previous periods. This means that the investment grows faster over time due to the compounding effect.
✅ Compound Interest Formula:
Where:
- A = Final amount
- P = Principal (starting amount)
- r = Interest rate (as a percentage)
- n = Number of years
📌 Example:
Imagine you invest £1,000 at 5% interest compounded annually for 3 years:
You’ve earned £1157.63 just from letting your money sit in an account and grow over time.
🔹 What Is Depreciation?
Depreciation refers to the reduction in value of an asset over time. It is most commonly expressed as a percentage and is often applied to real-life scenarios such as cars losing value, electronics becoming outdated, or machinery wearing out with use. Depreciation helps people and businesses understand the current value of an asset.
✅ Depreciation Formula:
Where the variables are the same as the compound interest formula, but represent a depreciation rate.
📌 Example:
A laptop worth £800 depreciates by 10% annually for 2 years:
This means the laptop would now be worth only £648 after two years.
🟢 Difference Between Compound Interest and Depreciation
While both compound interest and depreciation use similar formulas, they produce opposite outcomes. One reflects an increase in value, the other a decrease. Here’s a direct comparison:
| Feature | Compound Interest | Depreciation |
|---|---|---|
| Value Change | Increases | Decreases |
| Formula | A = P(1+r/100)^n | A = P(1-r/100)^n |
| Application | Savings, investments | Cars, electronics, equipment |
| Outcome Over Time | Growing balance | Shrinking value |
It’s important to clearly identify whether a problem is asking for an increase or decrease in value so you apply the correct formula.
📝 Practice Questions with Explanations
- A car worth £12,000 depreciates by 15% per year. What will it be worth after 3 years?
A = 12000(0.85^3) = £7731.00 - You invest £500 at 6% interest compounded annually. How much will you have in 5 years?
A = 500(1.06^5) = £669.11 - A phone is bought for £900. After 2 years at 20% annual depreciation, what’s its value?
A = 900(0.8^2) = £576.00 - How long will it take £1,000 to grow to £1,200 at 4% compound interest?
Use trial and error or logarithms to solve……..
These questions are similar to those found in AQA, Edexcel, and OCR GCSE Maths exams.
🔹 Tips for Solving Compound & Depreciation Questions
- Always convert rates to decimals (e.g., 6% becomes 0.06) before plugging them into the formula
- Use brackets carefully on calculators to avoid common input mistakes
- Check the compounding frequency: annual is typical in GCSE but monthly or daily may appear in real-world problems
- Draw a timeline of each year to track value changes
- Use estimation to check if your answer makes sense
- Start by writing the formula before you substitute any values. This reinforces the structure of your method.
🎯 Real-Life Applications of Compound Interest and Depreciation
Understanding compound interest and depreciation isn’t just about passing exams—it’s about being financially literate in the real world:
- Banking & Savings: Calculating returns on savings accounts and investments
- Loans & Mortgages: Understanding how interest builds on borrowed money
- Business Accounting: Estimating the current value of business equipment
- Personal Finance: Predicting how quickly cars and tech lose value
- Insurance & Tax: Calculating asset values for insurance claims and depreciation for tax deductions
This knowledge is fundamental for making informed decisions about money in both personal and professional life.
Explore more financial maths resources
✅ Final Thoughts
Whether you’re calculating how savings grow or how quickly an asset loses value, understanding compound interest and depreciation is vital for GCSE success and lifelong financial literacy. By mastering these formulas, practicing consistently, and reviewing real-world examples, you’ll be able to approach any financial maths problem with clarity and confidence.
For structured support, interactive lessons, and topic-specific exam preparation, visit GCSE Maths Tutor and start mastering your maths today.
