Simple & Compound Interest - Complete SSC CGL Guide
What are Simple & Compound Interest? These are methods of calculating interest on borrowed or invested money. Simple Interest (SI) calculates interest only on principal, while Compound Interest (CI) calculates interest on principal plus accumulated interest.
Simple Interest
Interest on principal only
Compound Interest
Interest on interest
Pro Tip – Master the Difference!
The key to solving SI-CI problems is understanding when to use which formula. CI grows faster than SI for the same rate and time. Visit SKY Practice for 500+ SI-CI questions with shortcuts.
1. Simple Interest Fundamentals
What is Simple Interest? Interest calculated only on the original principal amount throughout the loan/investment period.
SI Formulas & Key Concepts
Understanding Simple Interest
In SI, the interest amount remains constant every year. If ₹1000 earns ₹100 interest in first year at 10%, it will earn exactly ₹100 every year, not more.
Basic SI Formula
Where:
P = Principal (initial amount)
R = Rate of interest per annum (%)
T = Time period (years)
Amount Formula
Where A = Total amount after time T
A = 8000 + 1600 = ₹9600
Finding Principal/Rate/Time
R = (100×SI)/(P×T)
T = (100×SI)/(P×R)
SSC Shortcut: SI Calculation Tricks
For yearly SI: Interest for 1 year = (P×R)/100
Monthly interest: Divide annual interest by 12
Daily interest: Divide annual interest by 365
Quick percentage: 10% of P = P/10, 5% of P = P/20
Solved Example: SSC Pattern Question
Let P = ₹100, then A = ₹200 (doubles)
SI = A - P = ₹100
T = 5 years
R = (100×SI)/(P×T) = (100×100)/(100×5) = 20%
Method 2: Shortcut
For SI, if money doubles, SI = P
SI = (P×R×T)/100
P = (P×R×5)/100
1 = (R×5)/100
R = 100/5 = 20%
General Shortcut:
For SI: Time to double = 100/R years
For SI: Time to triple = 200/R years
Final Answer: 20% per annum
2. Compound Interest Concepts
What is Compound Interest? Interest calculated on the initial principal and also on the accumulated interest of previous periods.
CI Formulas & Methods
Understanding Compound Growth
In CI, each year's interest is added to the principal for the next year's calculation. This creates exponential growth - "interest on interest" effect.
Important CI Formulas
- Annual CI: A = P(1 + R/100)^T
- CI for 2 years: CI = P[(1+R/100)² - 1]
- CI for 3 years: CI = P[(1+R/100)³ - 1]
- CI for n years: CI = P[(1+R/100)^n - 1]
- When interest compounded half-yearly: Rate becomes R/2, Time becomes 2T
Common Mistakes
- Using SI formula for CI problems
- Forgetting to adjust rate for non-annual compounding
- Using wrong power for time period
- Calculating CI as P×R×T (that's SI!)
SSC Shortcut: CI for 2 and 3 Years
For 2 years at R%: CI = P(R/100)² + 2P(R/100)
Or faster: CI = P × R × (200 + R)/10000
For 3 years at R%: CI = P[(R/100)³ + 3(R/100)² + 3(R/100)]
Or: CI = P × R × (300R + 3R² + 10000)/1000000
Solved Example: Compound Interest Calculation
Year 1: P = ₹8000, Interest = 8000×5% = ₹400
Amount = ₹8400
Year 2: P = ₹8400, Interest = 8400×5% = ₹420
Amount = ₹8820
Year 3: P = ₹8820, Interest = 8820×5% = ₹441
Amount = ₹9261
CI = Final Amount - Principal = 9261 - 8000 = ₹1261
Method 2: Using formula (faster)
A = P(1 + R/100)^T = 8000(1 + 5/100)³
= 8000 × (1.05)³ = 8000 × 1.157625 = ₹9261
CI = 9261 - 8000 = ₹1261
Method 3: Using percentage method
3 years at 5% → Net effect = ?
Using successive percentage: 5% + 5% + 5% + (25+25+25)/100 + (125)/10000
= 15 + 0.75 + 0.0125 = 15.7625%
CI = 8000 × 15.7625/100 = ₹1261
All methods give same answer: ₹1261
3. Difference Between SI & CI
Key Distinction: SI grows linearly, CI grows exponentially. For same principal, rate and time, CI > SI.
SI vs CI Comparison
SSC Shortcut: Difference Between CI and SI
For 2 years at R%: CI - SI = P(R/100)²
For 3 years at R%: CI - SI = P(R/100)² × (3 + R/100)
Example: P=₹10000, R=10%, T=2 years
Difference = 10000 × (10/100)² = 10000 × 0.01 = ₹100
Principal: ₹1000
₹1100
+₹100 interest
₹1100
+₹100 interest
₹1200
+₹100 interest
₹1210
+₹110 interest
₹1300
+₹100 interest
₹1331
+₹121 interest
Solved Example: Difference Problem
For 2 years: CI - SI = P(R/100)²
Given: CI - SI = ₹20, R = 4%
20 = P × (4/100)²
20 = P × (0.04)²
20 = P × 0.0016
P = 20 / 0.0016 = ₹12,500
Verification:
SI for 2 years = (12500×4×2)/100 = ₹1000
CI for 2 years = 12500[(1+4/100)² - 1]
= 12500[(1.04)² - 1] = 12500[1.0816 - 1]
= 12500 × 0.0816 = ₹1020
Difference = 1020 - 1000 = ₹20 ✓
Final Answer: Principal = ₹12,500
4. Effective Annual Rate & Compounding
What is Effective Rate? The actual annual rate when interest is compounded more than once a year.
Effective Rate Formulas
Understanding Effective Rate
If bank says "10% per annum compounded semi-annually", the effective rate is more than 10% because interest is calculated twice a year.
Effective Annual Rate Formula
Where:
r = nominal annual rate (decimal)
n = number of compounding periods per year
Effective = (1 + 0.10/4)⁴ - 1
= (1.025)⁴ - 1 = 1.1038 - 1 = 0.1038
= 10.38%
Rule of 72
Quick estimation for doubling time:
Actual: ln(2)/ln(1.12) = 6.12 years
Rule of 114 & 144
For tripling and quadrupling:
Quadruple: ≈ 144 / Rate
Good for quick estimation in exams
SSC Shortcut: Effective Rate Comparison
Annual @ R% = R% effective
Semi-annual @ R% ≈ R% + (R²/200)%
Quarterly @ R% ≈ R% + (R²/133)%
Monthly @ R% ≈ R% + (R²/240)%
Example: 12% monthly ≈ 12% + (144/240)% = 12.6%
Solved Example: Effective Rate Calculation
Effective rate = (1 + 0.10/2)² - 1
= (1.05)² - 1 = 1.1025 - 1 = 0.1025 = 10.25%
Option 2: 10.25% compounded annually
Effective rate = 10.25% (since annual)
Comparison:
Both give exactly 10.25% effective rate!
General Principle:
r% compounded n times per year =
[n × 100 × ((1 + r/(100n))^n - 1)]% effective
Final Answer: Both are equally good
5. Different Compounding Periods
Compounding Frequency: How often interest is calculated and added to principal.
Compounding Formulas
SSC Shortcut: Quick Compounding Comparisons
More frequent = More interest (for same nominal rate)
Order: Daily > Monthly > Quarterly > Semi-annual > Annual
For quick comparison: Calculate effective rate using approximation formulas
Solved Example: Different Compounding Periods
A = 10000(1 + 8/100)² = 10000 × (1.08)²
= 10000 × 1.1664 = ₹11,664
(b) Compounded Semi-annually:
Rate per half-year = 8/2 = 4%
Number of periods = 2 × 2 = 4
A = 10000(1 + 4/100)⁴ = 10000 × (1.04)⁴
= 10000 × 1.16985856 = ₹11,698.59
(c) Compounded Quarterly:
Rate per quarter = 8/4 = 2%
Number of periods = 4 × 2 = 8
A = 10000(1 + 2/100)⁸ = 10000 × (1.02)⁸
= 10000 × 1.171659 = ₹11,716.59
Observation:
Annual: ₹11,664
Semi-annual: ₹11,698.59 (+₹34.59)
Quarterly: ₹11,716.59 (+₹52.59 vs annual)
More frequent compounding = Higher returns
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Frequently Asked Questions
Q1: How many SI-CI questions in SSC CGL?
Answer: Typically 4-6 questions in Tier I and 8-10 questions in Tier II. This topic has high weightage and questions range from basic calculations to complex difference problems.
Q2: What's the quickest way to find CI for 2 years?
Answer: Use formula: CI = P × R × (200 + R)/10000. For P=₹10000, R=10%: CI = 10000×10×210/10000 = ₹2100. Much faster than (1.1)² calculation.
Q3: How to remember the difference between CI and SI formulas?
Answer: SI is simple multiplication (P×R×T). CI has power/exponent (^T) because of compounding. For 2 years difference: CI-SI = P(R/100)² - remember the square!
Q4: What is the Rule of 72 and when to use it?
Answer: Rule of 72 estimates doubling time: 72/interest rate. At 12%, money doubles in ~6 years. Use for quick approximations in multiple choice questions.
Q5: How to handle half-yearly/quarterly compounding?
Answer: Divide rate by compounding frequency, multiply time by frequency. Semi-annual: R/2, 2T. Quarterly: R/4, 4T. Monthly: R/12, 12T.
Q6: When is CI equal to SI?
Answer: CI = SI only when time period is 1 year (no compounding effect) OR when principal is zero (trivial case). For T>1, CI > SI always for same P, R, T.
Final Exam Strategy for SI-CI Problems
Time Allocation: Basic problems: 30-40 seconds, Complex problems: 60-90 seconds.
Priority Order: 1) Direct formula application, 2) Difference problems, 3) Effective rate, 4) Different compounding periods.
Accuracy Check: Verify with SI first (easier calculation), then check if CI should be higher. Use approximation for quick verification.
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