Difference Between CI and SI

🎯 Learning Objective

Apply the 2-year and 3-year CI−SI difference formulas both ways.

💡 Concept

• For 2 years: CI − SI = P(r/100)²
• For 3 years: CI − SI = P(r/100)² × (3 + r/100)
• The 2-year gap is simply one year's interest ON year-1's interest
• Given the difference, find P: P = Difference × (100/r)²
• Year 1 difference is always zero

🧮 Key Formulas

2 years: CI − SI = P(r/100)²

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3 years: CI − SI = P(r/100)²(3 + r/100)

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P = Diff × (100/r)²

✏️ Easy Example

Q. Find the difference between CI and SI on ₹5,000 at 10% per annum for 2 years.

1. Diff = P(r/100)²
2. = 5000 × (0.1)²
3. = 5000 × 0.01

Answer: ₹50

🇮🇳 Real-Life Example

Two schemes both advertise 10% on your ₹5,000 — the compound one quietly pays ₹50 extra over 2 years. Small print, real money.

📝 Exam-Level Example

Q. The difference between CI and SI on a sum for 2 years at 5% per annum is ₹25. Find the sum.

1. P × (5/100)² = 25
2. P × 0.0025 = 25
3. P = 25 ÷ 0.0025

Answer: ₹10,000

📝 Exam-Level Example

Q. Find the difference between CI and SI on ₹8,000 at 10% per annum for 3 years.

1. Diff = P(r/100)²(3 + r/100)
2. = 8000 × 0.01 × 3.1

Answer: ₹248

🪄 Memory Trick

2-year difference in seconds: (r² × P)/10000. At 10% it is P/100; at 5% it is P/400.

⚠️ Common Mistakes

• ❌ Using the 2-year formula for a 3-year difference question
• ❌ Squaring r without dividing by 100 first
• ❌ Expecting a CI−SI difference in year 1 (it is zero)

🏆 Exam Tips

• ✅ 10% and 2 years → difference is exactly 1% of P — instant elimination in MCQs
• ✅ These difference questions are direct formula plugs — never expand year by year in the exam

📌 Summary

• 2 years: diff = P(r/100)²
• 3 years: diff = P(r/100)²(3 + r/100)
• Reverse: P = diff × (100/r)²
• Year 1 → CI = SI, difference zero