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.
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!
Worked Examples
Example 1: Savings Account
£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
Example 2: 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
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.
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