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Comparison of SI & CI

Introduction

Bank या exam problems में अक्सर Simple Interest (SI) और Compound Interest (CI) को compare करने के लिए पूछा जाता है। SI हमेशा original principal पर calculate होता है, जबकि CI हर साल new balance पर calculate होता है। इसी वजह से same time और rate पर CI हमेशा SI से ज्यादा होता है (1 year को छोड़कर)।

Pattern: Comparison of SI & CI

Pattern

Key concept: SI straight-line growth देता है, जबकि CI compounding से बढ़ता है।

- SI Formula: SI = (P × R × T) / 100
- CI Formula: CI = P(1 + R/100)^T - P
- Shortcut:
• 2 years के लिए → CI - SI = P × (R/100)²
• 3 years के लिए → CI - SI = P × (R/100)² × (3 + R/100)

Step-by-Step Example

Question

₹5,000 पर 10% per annum की दर से 2 years के लिए CI और SI का difference निकालें।

Options:
A. ₹0
B. ₹50
C. ₹100
D. ₹150

Solution

  1. Step 1: Given values लिखें

    Principal (P) = 5,000, Rate (R) = 10%, Time (T) = 2 years.

  2. Step 2: SI calculate करें

    SI = (P × R × T) / 100 = (5,000 × 10 × 2) / 100 = 1,000.

  3. Step 3: CI year-by-year निकालें (beginner method)

    1st year interest = (5,000 × 10) / 100 = 500 → Amount = 5,500
    2nd year interest = (5,500 × 10) / 100 = 550 → Amount = 6,050
    CI = 6,050 - 5,000 = 1,050

  4. Step 4: Difference निकालें

    Difference = CI - SI = 1,050 - 1,000 = 50

  5. Final Answer:

    ₹50 → Option B

  6. Quick Check:

    Shortcut (2 years): P × (R/100)² = 5,000 × (10/100)² = 5,000 × 0.01 = 50 ✅

Quick Variations

1. 1 year → SI = CI (difference = 0)

2. 2 years → Difference = P × (R/100)²

3. 3 years → Difference = P × (R/100)² × (3 + R/100)

4. अधिक years → Formula CI = P(1+R/100)^T - P use करें और SI subtract करें

Trick to Always Use

  • Step 1 → SI को direct formula से निकालें: (P×R×T)/100।
  • Step 2 → CI के लिए year-by-year या direct formula दोनों में से कोई भी तरीका use करें।
  • Step 3 → Difference = CI - SI निकालें।

Summary

Summary

  • SI हमेशा original principal पर होता है; CI हर साल बढ़े हुए amount पर।
  • 2 years वाले questions के लिए shortcut P × (R/100)² बहुत useful है।
  • Multi-year problems के लिए CI = P(1+R/100)^T - P use करें और फिर SI subtract करें।
  • Quick-check के लिए shortcut या yearly interest method का उपयोग करें।

Example to remember:
P = ₹5,000, R = 10%, T = 2 → CI - SI = ₹50 (Option B).

Practice

(1/5)
1. Find the difference between SI and CI on ₹2000 at 10% per annum for 2 years.
easy
A. ₹20
B. ₹25
C. ₹30
D. ₹40

Solution

  1. Step 1: Write given values

    P = 2000, R = 10%, T = 2 years.

  2. Step 2: Compute simple interest

    SI = (P × R × T)/100 = (2000 × 10 × 2)/100 = 400.

  3. Step 3: Apply 2-year shortcut

    Difference = P × (R/100)^2 = 2000 × (0.1 × 0.1) = 2000 × 0.01 = 20.

  4. Step 4: Optional CI computation

    CI = SI + Difference = 400 + 20 = 420.

  5. Final Answer:

    ₹20 → Option A.

  6. Quick Check:

    Year 1 interest = 200 → amount 2200. Year 2 interest = 220 → CI = 420. CI - SI = 20 ✅
Hint: For 2 years, use Difference = P × (R/100)^2.
Common Mistakes: Forgetting to square (R/100) or using SI instead of difference.
2. On ₹5000 at 8% per annum for 2 years, find the difference between CI and SI.
easy
A. ₹28
B. ₹32
C. ₹30
D. ₹34

Solution

  1. Step 1: Note principal, rate, and time

    P = 5000, R = 8%, T = 2 years.

  2. Step 2: Calculate SI

    SI = (5000 × 8 × 2)/100 = 800.

  3. Step 3: Use 2-year shortcut

    Difference = P × (R/100)^2 = 5000 × (0.08 × 0.08) = 5000 × 0.0064 = 32.

  4. Step 4: Compute CI

    CI = 800 + 32 = 832.

  5. Final Answer:

    ₹32 → Option B.

  6. Quick Check:

    Year 1 interest = 400 → amount 5400. Year 2 interest = 5400 × 8% = 432 → CI = 832. CI - SI = 32 ✅
Hint: Compute P × (R/100)^2 directly for 2-year difference.
Common Mistakes: Using R instead of R/100 or forgetting to square it.
3. Find the difference between SI and CI on ₹4000 at 12% per annum for 2 years.
easy
A. ₹54.50
B. ₹56
C. ₹57.60
D. ₹60

Solution

  1. Step 1: List known values

    P = 4000, R = 12%, T = 2 years.

  2. Step 2: Calculate SI

    SI = (4000 × 12 × 2)/100 = 960.

  3. Step 3: Use 2-year shortcut for difference

    Difference = 4000 × (0.12 × 0.12) = 4000 × 0.0144 = 57.6 → ₹57.60.

  4. Step 4: Compute CI

    CI = 960 + 57.60 = 1,017.60.

  5. Final Answer:

    ₹57.60 → Option C.

  6. Quick Check:

    Year 1 interest = 480 → amount = 4,480. Year 2 interest = 4,480 × 12% = 537.6 → CI = 1,017.6. Difference = 1,017.6 - 960 = 57.6 ✅
Hint: Keep two-decimal accuracy for non-integer differences.
Common Mistakes: Rounding too early or dropping decimals.
4. On ₹6000 at 5% per annum for 3 years, what is the difference between CI and SI?
medium
A. ₹42.50
B. ₹45.00
C. ₹46.25
D. ₹45.75

Solution

  1. Step 1: Write principal, rate, and time

    P = 6000, R = 5% (0.05), T = 3 years.

  2. Step 2: Compute SI

    SI = (6000 × 5 × 3)/100 = 900.

  3. Step 3: Apply 3-year CI-SI formula

    Difference = P × (R/100)^2 × (3 + R/100).

  4. Step 4: Evaluate stepwise

    (R/100)^2 = 0.05 × 0.05 = 0.0025. P × 0.0025 = 6000 × 0.0025 = 15. Multiply by (3 + 0.05) = 3.05 → 15 × 3.05 = 45.75.

  5. Final Answer:

    ₹45.75 → Option D.

  6. Quick Check:

    CI = 6000(1.05)^3 - 6000 = 6945.75 - 6000 = 945.75; CI - SI = 45.75 ✅
Hint: For 3 years, include extra multiplier (3 + R/100).
Common Mistakes: Dropping the +R/100 term or rounding mid-steps.
5. Find the difference between CI and SI on ₹10000 at 15% per annum for 2 years.
medium
A. ₹225
B. ₹220
C. ₹230
D. ₹240

Solution

  1. Step 1: Identify P, R, and T

    P = 10000, R = 15%, T = 2 years.

  2. Step 2: Calculate SI

    SI = (10000 × 15 × 2)/100 = 3000.

  3. Step 3: Apply shortcut for 2 years

    Difference = P × (R/100)^2 = 10000 × (0.15 × 0.15) = 10000 × 0.0225 = 225.

  4. Step 4: Compute CI

    CI = 3000 + 225 = 3225.

  5. Final Answer:

    ₹225 → Option A.

  6. Quick Check:

    CI = 10000(1.15)^2 - 10000 = 13225 - 10000 = 3225; CI - SI = 225 ✅
Hint: For 2-year CI-SI difference, simply compute P × (R/100)^2.
Common Mistakes: Not squaring the rate fraction or confusing SI with CI.

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