Simple Interest (சாதாரண வட்டி)

Simple Interest is one of the most frequently asked topics in competitive exams like TNPSC, SSC, Banking, and UPSC. Mastering Simple Interest helps you tackle 15-20% of quantitative aptitude questions and builds a strong foundation for compound interest, banking, and financial mathematics. Every rupee you earn or borrow involves interest calculations! 💰

---

🧠 Foundation: Understanding the Core Concept (அடிப்படை கருத்துகள்)

Simple Interest is the extra money paid for borrowing money or earned for lending money, calculated only on the original amount (principal). Think of it as a fixed rent for using money! 🏠💸

Real-world examples:

• 🏦 Bank deposits: You deposit ₹10,000, bank pays you interest
• 💳 Personal loans: You borrow ₹50,000, you pay interest to the lender
• 📱 EMI calculations: Understanding the interest component in your monthly payments

Core Formula Box:

The Core Formula

English: Simple Interest = (Principal × Rate × Time) ÷ 100
Tamil: சாதாரண வட்டி = (அசல் × வட்டி விகிதம் × காலம்) ÷ 100
Short Form: SI = (P × R × T) ÷ 100

---

Level 0: Formula Playground

Formula Variations Table

Component	English Formula	Tamil Formula	Symbol
Simple Interest	SI = (P × R × T) ÷ 100	சா.வ = (அ × வி × கா) ÷ 100	SI
Principal	P = (SI × 100) ÷ (R × T)	அசல் = (சா.வ × 100) ÷ (வி × கா)	P
Rate	R = (SI × 100) ÷ (P × T)	விகிதம் = (சா.வ × 100) ÷ (அ × கா)	R
Time	T = (SI × 100) ÷ (P × R)	காலம் = (சா.வ × 100) ÷ (அ × வி)	T
Amount	A = P + SI	மொத்தம் = அசல் + சா.வ	A

3 Simple Practice Drills

Drill 1: Find SI when P = ₹1,000, R = 5%, T = 2 years
Solution: SI = (1000 × 5 × 2) ÷ 100 = ₹100

Drill 2: Find Principal when SI = ₹200, R = 8%, T = 5 years
Solution: P = (200 × 100) ÷ (8 × 5) = ₹500

Drill 3: Find Amount when P = ₹5,000, R = 6%, T = 3 years
Solution: SI = (5000 × 6 × 3) ÷ 100 = ₹900, Amount = 5000 + 900 = ₹5,900

---

⚙️ Unit Conversion Mastery (அலகு மாற்றம்)

Common Conversion Mistakes

• Time confusion: Mixing months with years, days with years
• Rate confusion: Using 5% as 5 instead of 0.05 in decimal calculations
• Period mistakes: 3 years 4 months = 3.33 years (not 3.4 years)

Key Conversion Factors

From	To	Conversion
Months	Years	Divide by 12
Days	Years	Divide by 365
Years	Months	Multiply by 12
Percentage	Decimal	Divide by 100

3 Conversion Practice Problems

Problem 1: Convert 8 months to years
Solution: 8 ÷ 12 = 0.67 years (or 2/3 years)

Problem 2: Convert 2 years 6 months to years
Solution: 2 + (6 ÷ 12) = 2.5 years

Problem 3: If rate is 7.5%, what is it as a fraction?
Solution: 7.5% = 7.5/100 = 15/200 = 3/40

---

Level 1: Problem Reading Strategy (கேள்வியை அணுகும் முறை)

The G-F-V Framework

G (Given/கொடுக்கப்பட்டது): What information is provided?
F (Find/காண வேண்டியது): What are we asked to calculate?
V (Verify/சரிபார்ப்பு): Check if units match and answer makes sense

3 Simple Word Problems Using G-F-V

Problem 1: A person invests ₹8,000 at 12% per annum. Find the simple interest after 3 years.

G: Principal = ₹8,000, Rate = 12%, Time = 3 years
F: Simple Interest = ?
V: SI = (8000 × 12 × 3) ÷ 100 = ₹2,880 ✓

Problem 2: At what rate will ₹5,000 amount to ₹6,500 in 5 years?

G: Principal = ₹5,000, Amount = ₹6,500, Time = 5 years
F: Rate = ?
V: SI = 6500 - 5000 = ₹1,500, R = (1500 × 100) ÷ (5000 × 5) = 6% ✓

Problem 3: In how many years will ₹2,000 become ₹2,800 at 8% per annum?

G: Principal = ₹2,000, Amount = ₹2,800, Rate = 8%
F: Time = ?
V: SI = 2800 - 2000 = ₹800, T = (800 × 100) ÷ (2000 × 8) = 5 years ✓

---

Level 2: Pattern Recognition (கணக்குகளின் வகையை அறிதல்)

Pattern	English Keywords	Core Concept	Tamil Term
Basic SI	"find interest", "calculate SI"	Direct formula application	நேரடி வட்டி
Find Principal	"what sum", "initial amount"	Working backwards from SI	அசல் காணல்
Find Rate	"at what rate", "rate percent"	Calculate interest rate	வட்டி விகிதம் காணல்
Find Time	"in how many years", "time period"	Calculate duration	காலம் காணல்

Pattern 1: Basic SI Calculation (நேரடி வட்டி கணக்கு)

Keywords: "Find simple interest", "Calculate SI"
Core Insight: Direct application of SI = (P × R × T) ÷ 100

Visual: Principal → Rate × Time → Interest P ────→ R × T ────→ SI

Example: Find the simple interest on ₹12,000 at 15% per annum for 4 years.

• Given: P = ₹12,000, R = 15%, T = 4 years
• Formula: SI = (12000 × 15 × 4) ÷ 100 = ₹7,200

Pattern 2: Principal Finding (அசல் காணல்)

Keywords: "What sum", "Find principal", "Initial investment"
Core Insight: Work backwards using P = (SI × 100) ÷ (R × T)

Visual: Interest ← Rate × Time ← Principal SI ←──── R × T ←──── P

Example: What principal will earn ₹1,080 as simple interest in 3 years at 12% per annum?

• Given: SI = ₹1,080, R = 12%, T = 3 years
• Formula: P = (1080 × 100) ÷ (12 × 3) = ₹3,000

Pattern 3: Rate Finding (விகிதம் காணல்)

Keywords: "At what rate", "Find rate percent", "Rate of interest"
Core Insight: R = (SI × 100) ÷ (P × T)

Visual: Principal × Time → Interest → Rate P × T ────→ SI ────→ R

Example: At what rate will ₹6,000 earn ₹1,800 as simple interest in 5 years?

• Given: P = ₹6,000, SI = ₹1,800, T = 5 years
• Formula: R = (1800 × 100) ÷ (6000 × 5) = 6%

Pattern 4: Time Finding (காலம் காணல்)

Keywords: "In how many years", "Time period", "Duration"
Core Insight: T = (SI × 100) ÷ (P × R)

Visual: Principal × Rate → Interest → Time P × R ────→ SI ────→ T

Example: In how many years will ₹4,000 earn ₹960 as simple interest at 8% per annum?

• Given: P = ₹4,000, SI = ₹960, R = 8%
• Formula: T = (960 × 100) ÷ (4000 × 8) = 3 years

---

Level 3: Advanced Scenarios (சிக்கலான கணக்குகள்)

Scenario 1: Amount-based Problems

When given Amount instead of Simple Interest, remember: SI = Amount - Principal

Important Formula

Amount = Principal + Simple Interest
Therefore: Simple Interest = Amount - Principal

Example: ₹7,500 amounts to ₹9,000 in 4 years. Find the rate.

• SI = 9000 - 7500 = ₹1,500
• R = (1500 × 100) ÷ (7500 × 4) = 5%

Scenario 2: Fractional Time Periods

Handle months and days carefully by converting to years.

Example: Find SI on ₹3,000 at 10% for 2 years 8 months.

• Time = 2 + (8/12) = 2.67 years
• SI = (3000 × 10 × 2.67) ÷ 100 = ₹800

Conversion Tip

For exact calculations: 2 years 8 months = 2 + 8/12 = 32/12 years
SI = (3000 × 10 × 32) ÷ (100 × 12) = ₹800

---

⚠️ Common Beginner Mistakes (பொதுவான தவறுகள்)

Mistake 1: Time Unit Confusion

❌ Wrong: Using months directly in formula
✅ Correct: Convert months to years first

Mistake 2: Rate Percentage Error

❌ Wrong: Using 5% as 0.05 in the SI formula
✅ Correct: Use 5% as 5 in SI = (P × R × T) ÷ 100

Mistake 3: Amount vs Interest Confusion

❌ Wrong: Treating Amount as Simple Interest
✅ Correct: Simple Interest = Amount - Principal

Mistake 4: Formula Mixing

❌ Wrong: Using compound interest concepts in SI problems
✅ Correct: SI remains constant each year, no compounding

---

🚀 Key Takeaways (முக்கிய குறிப்புகள்)

1. Master the core formula: SI = (P × R × T) ÷ 100 - this solves 80% of problems
2. Unit conversions are crucial: Always convert months to years, ensure rate is in percentage
3. G-F-V approach: Given-Find-Verify prevents calculation errors
4. Amount ≠ Interest: Remember SI = Amount - Principal in amount-based problems
5. Practice pattern recognition: Identify keywords to choose the right formula variation

Success Formula

Practice Daily + Formula Mastery + Pattern Recognition = SI Success! 🎯

---

📝 Problems to Practice (பயிற்சிக் கேள்விகள்)

Pattern 1: Basic SI Calculation (3 problems)

Problem 1: Find the simple interest on ₹15,000 at 8% per annum for 5 years.
Pattern Identification: Direct SI calculation
Solution:

• Given: P = ₹15,000, R = 8%, T = 5 years
• Formula: SI = (P × R × T) ÷ 100
• SI = (15000 × 8 × 5) ÷ 100 = ₹6,000

Problem 2: Calculate the simple interest on ₹25,000 at 12% per annum for 3 years 6 months.
Pattern Identification: Direct SI with time conversion
Solution:

• Given: P = ₹25,000, R = 12%, T = 3.5 years (3 + 6/12)
• Formula: SI = (P × R × T) ÷ 100
• SI = (25000 × 12 × 3.5) ÷ 100 = ₹10,500

Problem 3: Find the simple interest on ₹8,500 at 15% per annum for 8 months.
Pattern Identification: Direct SI with month conversion
Solution:

• Given: P = ₹8,500, R = 15%, T = 8/12 = 2/3 years
• Formula: SI = (P × R × T) ÷ 100
• SI = (8500 × 15 × 2) ÷ (100 × 3) = ₹850

Pattern 2: Find Principal (3 problems)

Problem 4: What sum will earn ₹2,400 as simple interest in 6 years at 10% per annum?
Pattern Identification: Find principal from given SI
Solution:

• Given: SI = ₹2,400, R = 10%, T = 6 years
• Formula: P = (SI × 100) ÷ (R × T)
• P = (2400 × 100) ÷ (10 × 6) = ₹4,000

Problem 5: Find the principal if the simple interest for 4 years at 12% per annum is ₹1,920.
Pattern Identification: Principal calculation
Solution:

• Given: SI = ₹1,920, R = 12%, T = 4 years
• Formula: P = (SI × 100) ÷ (R × T)
• P = (1920 × 100) ÷ (12 × 4) = ₹4,000

Problem 6: What principal will amount to ₹13,200 in 5 years at 8% simple interest?
Pattern Identification: Principal from amount
Solution:

• Given: A = ₹13,200, R = 8%, T = 5 years
• Let P be the principal, then SI = (P × 8 × 5) ÷ 100 = 0.4P
• Amount = P + SI, so 13200 = P + 0.4P = 1.4P
• P = 13200 ÷ 1.4 = ₹9,429 (approximately)

Pattern 3: Find Rate (3 problems)

Problem 7: At what rate percent will ₹5,000 earn ₹1,500 as simple interest in 5 years?
Pattern Identification: Rate calculation from SI
Solution:

• Given: P = ₹5,000, SI = ₹1,500, T = 5 years
• Formula: R = (SI × 100) ÷ (P × T)
• R = (1500 × 100) ÷ (5000 × 5) = 6%

Problem 8: Find the rate if ₹12,000 amounts to ₹15,600 in 6 years at simple interest.
Pattern Identification: Rate from amount
Solution:

• Given: P = ₹12,000, A = ₹15,600, T = 6 years
• SI = A - P = 15600 - 12000 = ₹3,600
• Formula: R = (SI × 100) ÷ (P × T)
• R = (3600 × 100) ÷ (12000 × 6) = 5%

Problem 9: At what rate will ₹8,000 earn ₹960 as simple interest in 2 years?
Pattern Identification: Simple rate calculation
Solution:

• Given: P = ₹8,000, SI = ₹960, T = 2 years
• Formula: R = (SI × 100) ÷ (P × T)
• R = (960 × 100) ÷ (8000 × 2) = 6%

Pattern 4: Find Time (3 problems)

Problem 10: In how many years will ₹6,000 earn ₹1,440 as simple interest at 8% per annum?
Pattern Identification: Time calculation
Solution:

• Given: P = ₹6,000, SI = ₹1,440, R = 8%
• Formula: T = (SI × 100) ÷ (P × R)
• T = (1440 × 100) ÷ (6000 × 8) = 3 years

Problem 11: In how many years will ₹10,000 amount to ₹14,000 at 10% simple interest?
Pattern Identification: Time from amount
Solution:

• Given: P = ₹10,000, A = ₹14,000, R = 10%
• SI = A - P = 14000 - 10000 = ₹4,000
• Formula: T = (SI × 100) ÷ (P × R)
• T = (4000 × 100) ÷ (10000 × 10) = 4 years

Problem 12: In what time will ₹7,200 earn ₹1,080 as simple interest at 5% per annum?
Pattern Identification: Basic time calculation
Solution:

• Given: P = ₹7,200, SI = ₹1,080, R = 5%
• Formula: T = (SI × 100) ÷ (P × R)
• T = (1080 × 100) ÷ (7200 × 5) = 3 years