📚 Simple Interest - Complete Theory

Master Simple Interest concepts from basics to advanced with detailed explanations and solved examples.

🎯 What is Simple Interest?

Simple Interest (SI) is the interest calculated only on the principal amount for a given period at a given rate.

Key Characteristics:

• Interest is calculated only on the original principal
• Interest amount remains constant every year
• Easy to calculate compared to Compound Interest

📐 Basic Formula

Simple Interest (SI) = (P × R × T) / 100

Where:
P = Principal (Initial amount)
R = Rate of interest per annum (% per year)
T = Time period (in years)

Amount (A) = Principal + Simple Interest

A = P + SI
A = P + (P × R × T)/100
A = P[1 + (RT/100)]

🔍 Understanding Each Component

1. Principal (P)

• The original sum of money borrowed or invested
• Remains constant throughout the time period
• Also called the base amount or sum

Example: If you deposit ₹10,000 in a bank, then P = ₹10,000

2. Rate of Interest (R)

• Percentage charged per annum
• Always expressed as % per year unless specified
• Can be different for different periods (monthly, quarterly)

Example: If bank offers 5% p.a., then R = 5

3. Time Period (T)

• Duration for which money is borrowed/invested
• Must be in years for the standard formula
• Can be converted from months/days to years

Conversions:

• Months to Years: T = Months/12
• Days to Years: T = Days/365

Example:

• 6 months = 6/12 = 0.5 years
• 73 days = 73/365 = 0.2 years

📊 Derived Formulas

From the basic formula, we can derive:

Finding Principal (P):

P = (SI × 100) / (R × T)

Finding Rate (R):

R = (SI × 100) / (P × T)

Finding Time (T):

T = (SI × 100) / (P × R)

💡 Solved Examples

Example 1: Basic SI Calculation

Question: Find the simple interest on ₹5,000 at 8% per annum for 3 years.

Solution:

Given: P = ₹5,000, R = 8%, T = 3 years

SI = (P × R × T) / 100
SI = (5000 × 8 × 3) / 100
SI = 120,000 / 100
SI = ₹1,200

Amount = P + SI = 5000 + 1200 = ₹6,200

Answer: SI = ₹1,200, Amount = ₹6,200

Example 2: Finding Principal

Question: At what principal will the simple interest be ₹450 at 5% per annum for 3 years?

Solution:

Given: SI = ₹450, R = 5%, T = 3 years

P = (SI × 100) / (R × T)
P = (450 × 100) / (5 × 3)
P = 45,000 / 15
P = ₹3,000

Answer: Principal = ₹3,000

Example 3: Finding Rate

Question: At what rate percent per annum will ₹2,000 amount to ₹2,400 in 4 years?

Solution:

Given: P = ₹2,000, A = ₹2,400, T = 4 years

First find SI:
SI = A - P = 2400 - 2000 = ₹400

Now find R:
R = (SI × 100) / (P × T)
R = (400 × 100) / (2000 × 4)
R = 40,000 / 8,000
R = 5% per annum

Answer: Rate = 5% p.a.

Example 4: Finding Time

Question: In how many years will ₹3,600 become ₹4,320 at 4% simple interest?

Solution:

Given: P = ₹3,600, A = ₹4,320, R = 4%

First find SI:
SI = A - P = 4320 - 3600 = ₹720

Now find T:
T = (SI × 100) / (P × R)
T = (720 × 100) / (3600 × 4)
T = 72,000 / 14,400
T = 5 years

Answer: Time = 5 years

Example 5: Time in Months

Question: Find SI on ₹8,000 at 6% p.a. for 8 months.

Solution:

Given: P = ₹8,000, R = 6%, T = 8 months

First convert time to years:
T = 8/12 years = 2/3 years

SI = (P × R × T) / 100
SI = (8000 × 6 × 2/3) / 100
SI = (8000 × 6 × 2) / (100 × 3)
SI = 96,000 / 300
SI = ₹320

Answer: SI = ₹320

🔄 Important Variations

1. When Principal is Same, SI is Proportional to (R × T)

If two investments have same principal:

SI₁ / SI₂ = (R₁ × T₁) / (R₂ × T₂)

Example: P = ₹10,000 for both

• Investment A: 5% for 2 years → SI = ₹1,000
• Investment B: 10% for 1 year → SI = ₹1,000
• Ratio of (R₁T₁):(R₂T₂) = (5×2):(10×1) = 10:10 = 1:1 ✓

2. When Rate and Time are Same, SI is Proportional to Principal

SI₁ / SI₂ = P₁ / P₂

3. Equal SI on Two Different Principals

If SI is same on two different principals for same rate:

P₁ × T₁ = P₂ × T₂

📈 Real-Life Applications

1. Bank Deposits

When you deposit money in a savings account, banks pay simple interest on the principal amount.

2. Loans

Some personal loans use simple interest calculation for shorter periods.

3. Government Bonds

Certain government securities pay simple interest on the face value.

⚠️ Common Mistakes to Avoid

❌ Mistake 1: Not Converting Time to Years

Wrong: SI = (5000 × 6 × 6) / 100 for 6 months
Right: T = 6/12 = 0.5 years, then SI = (5000 × 6 × 0.5) / 100

❌ Mistake 2: Confusing Principal with Amount

Principal = Initial investment
Amount = Principal + Interest (Final value)

❌ Mistake 3: Wrong Formula Application

Wrong: SI = P × R × T (missing /100)
Right: SI = (P × R × T) / 100

🎯 Quick Tips & Shortcuts

Tip 1: Mental Calculation for Simple Cases

For R = 10%, T = 1 year:

SI = P/10

Tip 2: For R = 5%, T = 2 years:

SI = P/10 (same as above!)

Tip 3: Amount Shortcut

If SI = Principal, then:
Amount = 2 × Principal

🔗 Related Topics

Prerequisites:

• Percentage - Understanding % calculations
• Basic arithmetic operations

Next Level:

• Compound Interest - Interest on interest
• Time & Work - Uses similar proportion concepts

Practice:

• Simple Interest Practice Questions
• Formula Sheet

📝 Practice Problems

Level 1 (Basic):

1. Find SI on ₹2,500 at 4% p.a. for 5 years
2. What principal will give ₹600 as SI at 6% p.a. in 4 years?
3. At what rate will ₹1,000 amount to ₹1,200 in 5 years?

Level 2 (Intermediate):

4. ₹5,000 becomes ₹6,500 in 3 years. Find the rate of interest.
5. In how many years will ₹7,200 become ₹8,640 at 5% p.a.?
6. Find SI on ₹4,000 at 7.5% p.a. for 16 months.

Level 3 (Advanced):

7. A sum becomes 3 times itself in 20 years. Find the rate of interest.
8. Two equal sums were lent at 5% and 6% p.a. for 4 and 5 years respectively. If difference in SI is ₹180, find each sum.

Next Step: Practice 50+ questions to master this concept! 💪