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Difference SI vs CI

ITBP Constable · Quantitative Aptitude

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← Compound Interest Half-Yearly / Quarterly CI →

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Core Concept

Read this first — the foundation of the topic

→Core Concept

Simple Interest is calculated only on the principal amount throughout the investment period. Compound Interest is calculated on the principal plus accumulated interest from previous periods. The difference between CI and SI represents the 'extra earning' due to compounding effect

💡Key Formulas

For 2 years: CI - SI = P × R² / (100)² For 3 years: CI - SI = P × R² × (300 + R) / (100)³ Where P = Principal, R = Rate per annum, T = Time

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Exam Patterns

What examiners ask — read before attempting PYQs

📋SSC CGL typically asks three types of questions

(1) Direct calculation of difference given P, R, T (2) Finding principal when difference and rate are given (3) Finding rate when principal and difference are given. Most questions involve 2-3 years timeframe as longer periods make calculations complex

⚡Powerful Shortcut for 2 Years

Difference = (SI for 1 year)² / Principal This works because: If SI for 1 year = PRT/100, then difference = (PRT/100)² / P = PR²T²/(100²P) = PR²/100² (for T=2)

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Worked Example

Solve this step-by-step before moving on

1

Step 1

Calculate SI for 2 years SI = (P × R × T) / 100 = (8000 × 15 × 2) / 100 = Rs. 2400

2

Step 2

Calculate CI for 2 years Amount = P(1 + R/100)ᵀ = 8000(1 + 15/100)² = 8000 × (1.15)² = 8000 × 1.3225 = Rs. 10,580 CI = Amount - Principal = 10,580 - 8000 = Rs. 2580

3

Step 3

Find difference CI - SI = 2580 - 2400 = Rs. 180 Alternative (Using Formula): CI - SI = P × R² / (100)² = 8000 × (15)² / (100)² = 8000 × 225 / 10000 = Rs. 180 Quick Trick for 3 Years: For 3 years, the difference equals: 3 × (2-year difference) + (2-year difference × R/100) Common Mistake: Students often confuse the formula for different time periods. Remember: the 2-year formula is simplest and most tested. For 3 years, don't memorize the complex formula - use the relationship with 2-year difference instead.

🔑 Key Points

Difference exists only when time period is more than 1 year
For 2 years: CI - SI = P × R² / (100)²
For 3 years: CI - SI = P × R² × (300 + R) / (100)³
Difference represents interest earned on interest portions
2-year difference problems are most common in SSC CGL
If SI for 1 year is known, 2-year difference = (SI)² / Principal
Compound Interest is always greater than Simple Interest for same P, R, T
The difference increases exponentially with higher rates and longer periods

📌 Exam Facts

For 2 years at 10% rate, difference is always 1% of principal
For 2 years at 20% rate, difference is always 4% of principal
For Rs. 100 at 15% for 2 years, difference is exactly Rs. 2.25
The ratio CI:SI for 2 years at 10% is always 21:20
For 3 years, minimum additional factor in formula is 300 (when R=0)
Difference for 2 years = P×R²/10000 (direct calculation)
For equal principal and rate, 3-year difference is roughly 3 times 2-year difference
At 25% rate for 2 years, difference equals 6.25% of principal

🚀 60-Second Revision

Formula: 2 years difference = P × R² / 10000
Remember: Difference exists only when T > 1 year
Trick: 2-year difference = (Annual SI)² / Principal
Pattern: Most SSC questions use 2-3 year timeframes
Trap: Don't use 3-year formula for 2-year problems
Quick check: At 10% for 2 years, difference = 1% of principal
Method: Calculate both CI and SI separately when formulas confuse

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