Free Compound Interest Calculator with Steps
Calculate compound interest and depreciation with step-by-step working. Compare simple vs compound interest. Perfect for GCSE and A-Level maths exams.
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What is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. It's often called "interest on interest" and makes your money grow faster than simple interest.
In GCSE maths, compound interest questions are found in the "Ratio, proportion and rates of change" unit. You'll need to calculate both growth (compound interest) and decay (depreciation).
The Compound Interest Formula
A = P(1 + r/100)ⁿ
Key Concepts for GCSE
The Multiplier Method
Convert the percentage to a multiplier for quick calculations:
5% increase → multiplier = 1.05
12% increase → multiplier = 1.12
15% decrease → multiplier = 0.85
20% decrease → multiplier = 0.80
Simple vs Compound Interest
Simple Interest:
I = P × r × n / 100
Same interest each year
Compound Interest:
A = P(1 + r/100)ⁿ
Interest grows each year
Depreciation (Decay)
For decreasing values, subtract the rate from 1:
V = V₀(1 - r/100)ⁿ
Example: A car worth £10,000 depreciating at 15% per year
💡 Exam Tip
Always check whether the question asks for the final amount or just the interest/depreciation. If it asks for interest only, remember to subtract the principal from your answer!
How Compounding Frequency Affects Your Returns
See how £10,000 invested at 5% for 10 years grows differently depending on how often interest is compounded.
| Frequency | Times/Year | Final Amount | Interest Earned | Effective Rate |
|---|---|---|---|---|
| Annual | 1 | £16,288.95 | £6,288.95 | 5.000% |
| Semi-annual | 2 | £16,386.16 | £6,386.16 | 5.063% |
| Quarterly | 4 | £16,436.19 | £6,436.19 | 5.095% |
| Monthly | 12 | £16,470.09 | £6,470.09 | 5.116% |
| Daily | 365 | £16,486.65 | £6,486.65 | 5.127% |
| Continuous | ∞ | £16,487.21 | £6,487.21 | 5.127% |
More frequent compounding gives higher returns, but the difference gets smaller as frequency increases.
The Rule of 72 — Quick Mental Maths
Want to know how long it takes to double your money? Just divide 72 by the interest rate. No calculator needed!
Rule of 72 Quick Reference
When Is It Accurate?
The Rule of 72 is most accurate for rates between 2% and 15%, where the error is less than 1%.
At very low rates (below 2%), the rule slightly overestimates. At very high rates (above 15%), it increasingly underestimates.
For the exact answer, use: t = ln(2) / ln(1 + r/100)
Common Mistakes to Avoid
These are the most frequent errors students make in compound interest exam questions.
❌ Using simple interest formula instead of compound
A = 1000 + (1000 × 0.05 × 3) = £1,150
✔ Use A = P(1 + r/100)ⁿ for compound interest
A = 1000 × 1.05³ = £1,157.63
❌ Wrong multiplier for depreciation (1.15 instead of 0.85)
15% depreciation → multiplier = 1.15
✔ Subtract from 1 for depreciation
15% depreciation → multiplier = 1 - 0.15 = 0.85
❌ Forgetting to convert percentage (using 5 instead of 0.05)
Multiplier = 1 + 5 = 6
✔ Always divide by 100 first
Multiplier = 1 + 5/100 = 1.05
❌ Not raising to the power for multiple years
3 years: 1000 × 1.05 × 3 = £3,150
✔ Raise the multiplier to the power of n
3 years: 1000 × 1.05³ = £1,157.63
❌ Answering with total instead of just interest
"The interest is £1,157.63" (that's the total!)
✔ Read the question — subtract P if it asks for interest only
Interest = £1,157.63 - £1,000 = £157.63
❌ Ignoring compounding frequency
Monthly compounding: multiplier = 1.05, n = 3
✔ Adjust rate and periods for frequency
Monthly: rate = 5/12, periods = 3×12 = 36
Worked Examples
Basic Compound Interest
£2,000 is invested at 4% compound interest per year for 5 years. Find the final amount.
P = £2,000, r = 4%, n = 5
Multiplier = 1 + 4/100 = 1.04
A = 2000 × 1.04⁵
A = 2000 × 1.2166...
A = £2,433.31
Car Depreciation
A car worth £15,000 depreciates by 18% each year. Find its value after 3 years.
V₀ = £15,000, r = 18%, n = 3
Multiplier = 1 - 18/100 = 0.82
V = 15000 × 0.82³
V = 15000 × 0.5514...
V = £8,271.22
Monthly Contributions
You invest £100 per month at 6% annual interest (compounded monthly) for 25 years. Find the total value.
PMT = £100/month, r = 6%, n = 12, t = 25
Monthly rate = 6/12 = 0.5% = 0.005
Periods = 12 × 25 = 300
FV = 100 × ((1.005)³⁰⁰ - 1) / 0.005
FV = 100 × (4.4650 - 1) / 0.005
FV = £69,299.40
You deposited £30,000 — interest earned: £39,299.40
Finding the Rate
An investment of £5,000 grows to £7,500 over 8 years. Find the annual interest rate.
P = £5,000, A = £7,500, n = 8
A/P = 7500/5000 = 1.5
⁸√1.5 = 1.5^(1/8) = 1.05199...
r = (1.05199 - 1) × 100
r = 5.20% per year
When to Use Each Formula
Quick reference guide for choosing the right formula in exam questions.
"I know P, r, n — find A"
Compound Interest
A = P(1+r/100)ⁿ
"Value is decreasing"
Depreciation
V = V₀(1-r/100)ⁿ
"I'm adding money regularly"
Contributions
FV = P(1+r/n)^nt + PMT×...
"I know start & end values"
Find Rate
r = 100×(ⁿ√(A/P) - 1)
"How long until I reach X?"
Find Time
n = log(A/P) / log(base)
"Quick mental estimate"
Rule of 72
t ≈ 72 / r
Frequently Asked Questions
What is the compound interest formula?
A = P(1 + r/100)ⁿ where A = final amount, P = principal, r = rate (%), n = years. For 5% interest, the multiplier is 1.05.
What's the difference between simple and compound interest?
Simple interest is calculated only on the original amount. Compound interest is calculated on the amount plus previously earned interest, so it grows faster over time.
How do I calculate depreciation?
Use V = V₀(1 - r/100)ⁿ. For depreciation, subtract the rate from 1. A 15% depreciation gives a multiplier of 0.85.
What does "compounding frequency" mean?
How often interest is calculated and added. Annual = once per year, monthly = 12 times per year. More frequent compounding gives slightly higher returns.
How do I find the rate if I know start and end values?
Use r = 100 × (ⁿ√(A/P) - 1). Divide final by initial, take the nth root, subtract 1, multiply by 100.
Is this aligned with the GCSE syllabus?
Yes! Covers Edexcel, AQA, and OCR compound interest and depreciation topics. Shows full working as expected in exam answers.
What is the Rule of 72?
A quick mental shortcut: divide 72 by the interest rate to estimate how long it takes to double your money. At 6%, it takes about 72 ÷ 6 = 12 years. Works best for rates between 2% and 15%.
How do monthly contributions affect compound interest?
Each monthly deposit earns compound interest from the moment it is added. Over long periods, contributions combined with compound growth create dramatic results — often doubling or tripling the total amount deposited.
What is the difference between nominal and real interest rates?
Nominal rate is the stated interest rate. Real rate adjusts for inflation, showing actual purchasing power gain. If you earn 5% but inflation is 2%, your real return is about 3%.
How does compounding frequency affect returns?
More frequent compounding means interest is added to the principal sooner, earning "interest on interest" faster. Monthly vs annual compounding on £10,000 at 5% for 10 years yields about £181 extra.
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