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Compound Interest

Compound Interest (CI) problems involve interest calculated on the principal plus accumulated interest from previous periods. These problems test your understanding of exponential growth and compounding frequency.

10Worksheets
200+Practice Questions
IntermediateDifficulty
3-4 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Compound Interest

Compound Interest (CI) problems involve interest calculated on the principal plus accumulated interest from previous periods. These problems test your understanding of exponential growth and compounding frequency.

Prerequisites

Simple Interest concepts Percentage calculation Exponents Amount formula: A = P(1 + r/100)^n
Why This Matters: Compound Interest problems appear in 2-3 questions in SSC CGL and Banking PO exams. They are essential for financial mathematics.

How to Solve Compound Interest Problems

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Step 1: Identify P (principal), R (rate%), T (time), and compounding frequency

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Step 2: For annual compounding: A = P(1 + R/100)^T

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Step 3: For half-yearly: A = P(1 + R/200)^(2T)

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Step 4: For quarterly: A = P(1 + R/400)^(4T)

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Step 5: Calculate Compound Interest: CI = A - P

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Step 6: For finding rate or time, use logarithms or trial

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Step 7: For CI-SI difference, use formulas for 2 and 3 years

Pro Strategy: Always identify the compounding frequency first. Use the appropriate formula. For 2 years, CI = P(1 + R/100)² - P = P(2R/100 + R²/10000).

Example Problem

Example: Find compound interest on ₹10000 at 10% per annum for 2 years, compounded annually. Solution: Step 1: P = 10000, R = 10%, T = 2 Step 2: A = 10000(1 + 10/100)² Step 3: = 10000(1.1)² = 10000 × 1.21 = 12100 Step 4: CI = A - P = 12100 - 10000 = 2100 Answer: ₹2100

Pro Tips & Tricks

  • CI for 2 years = P(2R/100 + R²/10000)
  • CI for 3 years = P(3R/100 + 3R²/10000 + R³/1000000)
  • CI-SI difference for 2 years = P(R/100)²
  • CI-SI difference for 3 years = P(R/100)²(3 + R/100)
  • When rate is compounded half-yearly, R becomes R/2, T becomes 2T
  • When rate is compounded quarterly, R becomes R/4, T becomes 4T

Shortcut Methods to Solve Faster

A = P(1 + r/100)ⁿ
CI = P[(1 + r/100)ⁿ - 1]
For half-yearly: A = P(1 + r/200)²ⁿ
For quarterly: A = P(1 + r/400)⁴ⁿ

Common Mistakes to Avoid

Using SI formula for CI
Forgetting to adjust rate and time for different compounding frequencies
Confusing CI with amount
Not subtracting principal to get CI

Exam Importance

Compound Interest is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
1-2 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Compound Interest?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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