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Basic SI Calculation

Introduction

Simple Interest (SI) is the extra money paid or earned on a principal amount over a period of time at a fixed rate. This is the most basic concept in interest problems and forms the foundation for advanced patterns.

Pattern: Basic SI Calculation

Pattern

The formula is: SI = (P × R × T) / 100

Where:
P = Principal (initial amount)
R = Rate of interest (per annum)
T = Time (in years)

Step-by-Step Example

Question

Find the Simple Interest on ₹5000 at 10% per annum for 2 years.

Options:
A. ₹800
B. ₹900
C. ₹1000
D. ₹1200

Solution

  1. Step 1: Identify the values

    P = 5,000, R = 10%, T = 2 years.

  2. Step 2: Apply the formula

    SI = (P × R × T) / 100.

  3. Step 3: Calculate the interest

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

  4. Final Answer:

    ₹1,000 → Option C

  5. Quick Check:

    Interest for 1 year = 10% of 5,000 = 500. For 2 years → 500 × 2 = 1,000 ✅

Quick Variations

1. Change the time period (months → convert to years).

2. Interest may be asked in fractional years (e.g., 6 months = 0.5 years).

3. Sometimes directly ask for total amount = Principal + SI.

Trick to Always Use

  • Step 1 → Write the formula clearly.
  • Step 2 → Plug values directly, avoid mental shortcuts.
  • Step 3 → For month-based questions, convert months to years before applying formula.

Summary

Summary

  • Use SI = (P × R × T) / 100 for all simple interest problems.
  • Keep P in rupees, R in percent, and T in years for correct calculation.
  • Convert months to years whenever required.
  • Verify by checking yearly interest × number of years.

Example to remember:
On ₹5,000 at 10% per annum for 2 years, SI = ₹1,000.

Practice

(1/5)
1. Find the Simple Interest on ₹2000 at 5% per annum for 2 years.
easy
A. 200
B. 250
C. 180
D. 300

Solution

  1. Step 1: Note the given values

    P = 2,000, R = 5%, T = 2.

  2. Step 2: Apply the SI formula

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

  3. Step 3: Calculate the interest

    SI = 200.

  4. Final Answer:

    200 → Option A

  5. Quick Check:

    Yearly interest = 2,000 × 5% = 100; for 2 years → 100 × 2 = 200 ✅
Hint: Multiply the yearly interest (P×R/100) by the number of years.
Common Mistakes: Forgetting to convert rate/time or dividing by 2 instead of multiplying time.
2. Calculate the SI on ₹4000 at 8% per annum for 1 year.
easy
A. 280
B. 320
C. 300
D. 360

Solution

  1. Step 1: Write the known values

    P = 4,000, R = 8%, T = 1.

  2. Step 2: Apply SI formula

    SI = (4,000 × 8 × 1)/100 = 320.

  3. Final Answer:

    320 → Option B

  4. Quick Check:

    8% of 4,000 = 0.08 × 4,000 = 320 ✅
Hint: For 1 year, use SI = (P × R) / 100 directly.
Common Mistakes: Forgetting that time = 1 year or using incorrect rate conversion.
3. Find the SI on ₹6000 at 12% per annum for 6 months.
easy
A. 720
B. 600
C. 500
D. 360

Solution

  1. Step 1: Convert time properly

    P = 6,000, R = 12%, T = 6 months = 0.5 year.

  2. Step 2: Use SI formula

    SI = (6,000 × 12 × 0.5)/100.

  3. Step 3: Perform the calculation

    SI = (6,000 × 6)/100 = 360.

  4. Final Answer:

    360 → Option D

  5. Quick Check:

    Yearly SI = 12% of 6,000 = 720; half-year = 720 ÷ 2 = 360 ✅
Hint: Convert months to years (6 months = 0.5 year) before applying the formula.
Common Mistakes: Taking 6 months as 6 years or forgetting to divide by 12.
4. A sum of ₹5000 is lent at 9% per annum for 4 years. Find the Simple Interest.
medium
A. 1800
B. 1600
C. 1400
D. 2000

Solution

  1. Step 1: Extract the values

    P = 5,000, R = 9%, T = 4.

  2. Step 2: Apply the SI formula

    SI = (5,000 × 9 × 4)/100.

  3. Step 3: Calculate SI

    SI = (5,000 × 36)/100 = 1,800.

  4. Final Answer:

    1,800 → Option A

  5. Quick Check:

    Yearly SI = 5,000 × 9% = 450; for 4 years → 450 × 4 = 1,800 ✅
Hint: Compute yearly interest first (P×R/100), then multiply by years.
Common Mistakes: Mixing up principal and total amount or adding principal to SI.
5. If ₹8000 is invested at 7.5% per annum for 3 years, what is the Simple Interest?
medium
A. 1600
B. 1700
C. 1800
D. 2000

Solution

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

    P = 8,000, R = 7.5%, T = 3.

  2. Step 2: Apply SI formula

    SI = (8,000 × 7.5 × 3)/100.

  3. Step 3: Compute the value

    SI = (8,000 × 22.5)/100 = 1,800.

  4. Final Answer:

    1,800 → Option C

  5. Quick Check:

    Yearly SI = 7.5% of 8,000 = 600; for 3 years → 600 × 3 = 1,800 ✅
Hint: Convert decimal % (7.5%) correctly as 7.5 before multiplying.
Common Mistakes: Rounding 7.5% incorrectly or forgetting to multiply by 3 years.

Mock Test

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