Compound Interest Basics

🎯 Learning Objective

Use A = P(1 + r/100)ⁿ to find amount and compound interest.

💡 Concept

• Amount A = P(1 + r/100)ⁿ; CI = A − P
• In CI, each year's interest is added to the principal — interest starts earning interest
• Year 1: CI = SI; the gap opens from year 2 onwards
• For 2 years, effective rate = 2r + r²/100 (the successive-change formula)
• Multiply year by year: 10% for 2 years → × 1.1 × 1.1

🧮 Key Formulas

A = P(1 + r/100)ⁿ

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CI = A − P

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2-year effective rate = 2r + r²/100

✏️ Easy Example

Q. Find the compound interest on ₹10,000 at 10% per annum for 2 years.

1. A = 10000 × 1.1 × 1.1
2. = 12100
3. CI = 12100 − 10000

Answer: ₹2,100

🇮🇳 Real-Life Example

A ₹10,000 FD at 10%: year 1 pays ₹1,000 but year 2 pays ₹1,100 — because last year's interest also joined the earning team.

📝 Exam-Level Example

Q. Find the compound interest on ₹8,000 at 5% per annum for 2 years.

1. 8000 × 1.05 = 8400
2. 8400 × 1.05 = 8820
3. CI = 8820 − 8000

Answer: ₹820

📝 Exam-Level Example

Q. A sum of ₹5,000 amounts to ₹6,655 in 3 years at compound interest. Find the rate per annum.

1. (1 + r/100)³ = 6655/5000 = 1.331
2. 1.331 = (1.1)³
3. r = 10

Answer: 10%

🪄 Memory Trick

For 2 years use 2r + r²/100 directly: 10% → 21%, 5% → 10.25%, 20% → 44%. One multiplication finishes the question.

⚠️ Common Mistakes

• ❌ Using the SI formula P×r×n/100 for compound questions
• ❌ Reporting the amount A when the question asks for CI
• ❌ Adding 10% + 10% = 20% for two years instead of 21%

🏆 Exam Tips

• ✅ Memorise powers of 1.1: 1.21, 1.331 — they appear every year
• ✅ 1.331 seen anywhere → rate is 10% for 3 years

📌 Summary

• A = P(1 + r/100)ⁿ, CI = A − P
• Interest earns interest from year 2
• 2-year shortcut: 2r + r²/100
• Year 1 CI = year 1 SI