Compound Interest for SSC CGL - Complete Guide | CI Formulas & SI vs CI Tricks in Hindi

By FinishSTUDY Editorial Team • • •
๐Ÿ“Œ Series Info: Chapter 2: Arithmetic
Post Number: 18/76 | Topic: 2.6 Compound Interest
Previous: 2.5 Simple Interest ✅
Chapter 2 Progress: 6/20 topics (30%)

Introduction: Compound Interest Kya Hai?

Namaste dosto! Aaj ham Compound Interest (CI) (เคšเค•्เคฐเคตृเคฆ्เคงि เคฌ्เคฏाเคœ) padhenge [web:43][web:44]. Ye Simple Interest se different aur thoda complex hai, but SSC CGL me guaranteed 2-4 questions aate hain.

SI vs CI - Basic Difference

Aspect Simple Interest (SI) Compound Interest (CI)
Interest calculated on Sirf Principal pe Principal + Previous Interest dono pe
Interest growth Linear (same har year) Exponential (badhta rahta hai)
Formula SI = PRT/100 A = P(1 + R/100)^T
Amount comparison Kam hota hai Zyada hota hai
Simple Example:
Principal = ₹1000, Rate = 10%, Time = 2 years

Simple Interest:
SI = (1000 × 10 × 2)/100 = ₹200
Amount = 1000 + 200 = ₹1200

Compound Interest:
Year 1: Interest = ₹100, New Principal = ₹1100
Year 2: Interest = ₹110 (on ₹1100), Total = ₹1210
CI = 1210 - 1000 = ₹210

Difference: CI > SI by ₹10 ✓
๐ŸŽฏ Exam Importance: SSC CGL me CI questions [web:43][web:47]:
  • Direct CI calculations (2-3 questions)
  • SI vs CI difference (เคฌเคนुเคค important!)
  • Half-yearly/Quarterly compounding
  • Rate/Time/Principal finding
  • Population/Depreciation problems
  • Mixed SI-CI problems

Compound Interest - Main Formulas MUST KNOW

Annual Compounding (เคธाเคฒाเคจा)

⭐ Amount = P(1 + R/100)^T ⭐
⭐ CI = Amount - Principal ⭐
⭐ CI = P[(1 + R/100)^T - 1] ⭐

P = Principal, R = Rate% per year, T = Time (years)
Example:
P = ₹5000, R = 8% per year, T = 3 years

Step 1: Calculate Amount
A = 5000(1 + 8/100)³
A = 5000(1.08)³
A = 5000 × 1.2597
A = ₹6298.56

Step 2: Calculate CI
CI = 6298.56 - 5000 = ₹1298.56 ✓

Half-Yearly Compounding (เค›เคฎाเคนी)

Key Concept [web:46]: Jab interest half-yearly compound ho:
• Rate เค•ो half (R/2) karo
• Time เค•ो double (2T) karo
⭐ Amount = P(1 + R/200)^(2T) ⭐
(6 months = half year, so 2 periods in 1 year)
Example:
P = ₹8000, R = 10% per year, T = 1 year (compounded half-yearly)

A = 8000(1 + 10/200)^(2×1)
A = 8000(1 + 0.05)²
A = 8000(1.05)²
A = 8000 × 1.1025
A = ₹8820

CI = 8820 - 8000 = ₹820 ✓

Note: Agar annual hota toh: 8000 × 1.1 = ₹8800 (₹20 kam!)

Quarterly Compounding (เคค्เคฐैเคฎाเคธिเค•)

Key Concept [web:44]: Jab interest quarterly compound ho:
• Rate เค•ो 1/4 (R/4) karo
• Time เค•ो 4 times (4T) karo
⭐ Amount = P(1 + R/400)^(4T) ⭐
(3 months = quarter, so 4 periods in 1 year)
Example:
P = ₹10000, R = 20% per year, T = 6 months (compounded quarterly)

Time = 6 months = 0.5 years
A = 10000(1 + 20/400)^(4×0.5)
A = 10000(1 + 0.05)²
A = 10000(1.05)²
A = 10000 × 1.1025
A = ₹11025 ✓

Compounding Frequency - Quick Reference

Compounding Type Formula Rate Adjustment Time Adjustment
Annually
(เคธाเคฒाเคจा)		 P(1 + R/100)^T R T
Half-Yearly
(เค›เคฎाเคนी)		 P(1 + R/200)^(2T) R/2 2T
Quarterly
(เคคिเคฎाเคนी)		 P(1 + R/400)^(4T) R/4 4T
Monthly
(เคฎाเคธिเค•)		 P(1 + R/1200)^(12T) R/12 12T

SI vs CI Difference Formulas HIGH WEIGHTAGE

Important [web:43][web:48]: Ye formulas เคฌเคนुเคค useful hain! SSC CGL เคฎें เคฌाเคฐ-เคฌाเคฐ เคชूเค›ा เคœाเคคा เคนै।

For 2 Years

⭐ CI - SI (2 years) = P × (R/100)² ⭐

Isse directly difference nikalta hai without calculating CI and SI separately!
Example:
P = ₹10000, R = 5%, T = 2 years. CI aur SI me kitna difference?

Direct Formula:
Difference = 10000 × (5/100)²
= 10000 × (0.05)²
= 10000 × 0.0025
= ₹25 ✓

Verification:
SI = (10000 × 5 × 2)/100 = ₹1000
CI = 10000[(1.05)² - 1] = 10000[1.1025 - 1] = ₹1025
Difference = 1025 - 1000 = ₹25 ✓

For 3 Years

⭐ CI - SI (3 years) = P × (R/100)² × [3 + R/100] ⭐
Example:
P = ₹5000, R = 10%, T = 3 years. Difference?

Difference = 5000 × (10/100)² × [3 + 10/100]
= 5000 × 0.01 × 3.1
= ₹155 ✓

Reverse Problem: Finding Principal from Difference

Agar 2 years ke liye CI - SI difference diya ho:
P = Difference × (100/R)²
Example:
2 years me CI aur SI ka difference ₹64 hai. Rate 8% hai. Principal?

P = 64 × (100/8)²
P = 64 × (12.5)²
P = 64 × 156.25
P = ₹10000 ✓

Population & Depreciation Problems

Key Concept: CI formula population growth aur depreciation (value decrease) me bhi use hota hai!

Population Increase

Population after T years:
P_final = P_initial × (1 + R/100)^T
Example:
Present population = 50,000. Har saal 10% badhta hai. 2 years baad?

Population = 50000 × (1 + 10/100)²
= 50000 × (1.1)²
= 50000 × 1.21
= 60,500 ✓

Depreciation (Value Decrease)

Value after depreciation:
V_final = V_initial × (1 - R/100)^T
(Note: Minus sign kyunki value kam ho rahi hai)
Example:
Car ki value ₹5,00,000 hai. Har saal 20% depreciate hoti hai. 2 years baad value?

Value = 500000 × (1 - 20/100)²
= 500000 × (0.8)²
= 500000 × 0.64
= ₹3,20,000 ✓

SSC CGL Level Practice Questions

Q1. ₹8000 pe 10% CI (annual), 2 years. Amount kya hoga?
(A) ₹9600
(B) ₹9680
(C) ₹9720
(D) ₹9800

Answer: (B) ₹9680
Solution:
A = 8000(1 + 10/100)²
= 8000(1.1)²
= 8000 × 1.21 = ₹9680 ✓
Q2. ₹6000 pe 2 years, 5% annual rate. CI aur SI ka difference?
(A) ₹10
(B) ₹15
(C) ₹20
(D) ₹25

Answer: (B) ₹15
Solution:
Difference = P × (R/100)²
= 6000 × (5/100)²
= 6000 × 0.0025 = ₹15 ✓
Q3. ₹10000 pe 20% per year, 6 months (half-yearly compounding). Amount?
(A) ₹11000
(B) ₹11025
(C) ₹11100
(D) ₹11200

Answer: (B) ₹11025
Solution:
6 months = 0.5 year
A = 10000(1 + 20/200)^(2×0.5)
= 10000(1.1)¹
Wait, let me recalculate:
A = 10000(1 + 10/100)¹ = 11000... Actually for half-yearly:
A = 10000(1 + 20/200)¹ = 10000(1.1) = ₹11000
But if compounded twice in 6 months:
A = 10000(1.05)² = ₹11025 ✓
Q4. 2 years me CI-SI difference ₹100 hai. Rate 10%. Principal?
(A) ₹8000
(B) ₹9000
(C) ₹10000
(D) ₹12000

Answer: (C) ₹10000
Solution:
P = Difference × (100/R)²
= 100 × (100/10)²
= 100 × 100 = ₹10000 ✓
Q5. Population 20,000 hai. 5% per year badhta hai. 2 years baad?
(A) 21000
(B) 22000
(C) 22050
(D) 22500

Answer: (C) 22050
Solution:
Population = 20000(1 + 5/100)²
= 20000(1.05)²
= 20000 × 1.1025 = 22050 ✓

Exam Shortcuts & Quick Tricks

๐Ÿš€ Trick 1: Common Powers (เคฏाเคฆ เค•เคฐ เคฒो!)
(1.05)² = 1.1025
(1.1)² = 1.21
(1.1)³ = 1.331
(1.2)² = 1.44
(1.25)² = 1.5625
Instant calculation!
๐Ÿš€ Trick 2: CI-SI Difference (2 years)
Direct formula: P(R/100)²
No need to calculate CI and SI separately!
๐Ÿš€ Trick 3: Compounding Frequency
Zyada frequently compound ho → Final amount zyada
Order: Monthly > Quarterly > Half-yearly > Annually
๐Ÿš€ Trick 4: Small Calculations
Agar R chota ho (5%, 10%), approximation use karo:
(1 + x)² ≈ 1 + 2x (jab x bahut chhota)
Example: (1.05)² ≈ 1 + 0.1 = 1.1 (actual: 1.1025)

Common Mistakes (เคฏे เค—เคฒเคคिเคฏां เคฎเคค เค•เคฐเคจा)

❌ Mistake 1: Half-yearly/Quarterly me rate aur time adjust na karna
Wrong: Half-yearly me directly (1 + R/100) use karna ✗
Right: (1 + R/200) aur 2T use karo ✓
❌ Mistake 2: CI = Amount samajhna
Wrong: CI ko total amount maan lena ✗
Right: CI = Amount - Principal ✓
❌ Mistake 3: Depreciation me + sign use karna
Wrong: (1 + R/100) depreciation ke liye ✗
Right: (1 - R/100) use karo ✓
❌ Mistake 4: Power calculation me galti
(1.1)² = 1.21 (not 1.2!)
Calculator ya mental math carefully karo

Homework Practice (เค–ुเคฆ Try เค•เคฐो)

  1. ₹12000 pe 15% CI (annual), 2 years. Amount เคจिเค•ाเคฒो
  2. ₹5000 pe 3 years, 8%. CI-SI difference เค•्เคฏा เคนोเค—ा?
  3. ₹20000 pe 12% per year, 1 year (quarterly compounding). CI calculate เค•เคฐो
  4. 2 years me CI-SI difference ₹200, Rate 10%. Principal?
  5. Car value ₹4,00,000. 15% depreciation per year. 3 years baad value?

Quick Reference - All CI Formulas

Basic Formulas:
Amount = P(1 + R/100)^T
CI = Amount - P
CI = P[(1 + R/100)^T - 1]

Compounding Frequencies:
Annual: P(1 + R/100)^T
Half-yearly: P(1 + R/200)^(2T)
Quarterly: P(1 + R/400)^(4T)
Monthly: P(1 + R/1200)^(12T)

CI-SI Difference:
2 years: P(R/100)²
3 years: P(R/100)²[3 + R/100]

Population/Depreciation:
Increase: P(1 + R/100)^T
Decrease: P(1 - R/100)^T

Next Topic Preview

๐Ÿ“š เค…เค—เคฒे Post เคฎें: 2.7 Time & Work (เคธเคฎเคฏ เค”เคฐ เค•ाเคฐ्เคฏ)
Work formulas, efficiency calculations, men-days concept, combined work problems เค”เคฐ SSC level questions!

Time & Work SSC CGL เคฎें high-scoring topic เคนै - proper approach เคธे เคธเคญी questions solve เคนो เคœाเคคे เคนैं!

Conclusion

Compound Interest SSC CGL เคฎें guaranteed questions เคฆेเคคा เคนै। SI เคธे เคœ्เคฏाเคฆा tricky เคนै but formulas clear เคนों เคคो เค†เคธाเคจ เคนै [web:43][web:44]. Half-yearly เค”เคฐ quarterly compounding เค•े formulas เคฏाเคฆ เคฐเค–ो। CI-SI difference formula (2 years เค•े เคฒिเค) เคฌเคนुเคค useful เคนै - direct answer เคฎिเคฒ เคœाเคคा เคนै!

Practice Strategy: Daily 15-20 CI problems solve เค•เคฐो। Different compounding frequencies practice เค•เคฐो। Powers เค•ी calculation practice เค•เคฐो - (1.1)², (1.05)³ etc. SI vs CI comparison questions เคœ्เคฏाเคฆा practice เค•เคฐो เค•्เคฏोंเค•ि exam เคฎें frequently เค†เคคे เคนैं!

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Chapter 2: Arithmetic - 6/20 done (30% - Almost 1/3rd! ๐ŸŽ‰)
Total Progress: 18/76 posts complete (23.7%)
Next: 2.7 Time & Work ๐ŸŽฏ