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When the interest is calculated annually...

When the interest is calculated annually, simple interest and compound interest are equal for the first year.

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To solve the question, we need to compare the Simple Interest (SI) and Compound Interest (CI) for the first year when calculated annually. Let's go through the steps: ### Step-by-Step Solution: 1. **Define the Principal Amount (P)**: - Let's assume the principal amount is \( P = 100 \) rupees. 2. **Define the Rate of Interest (R)**: - Assume the rate of interest is \( R = 5\% \). 3. **Define the Time Period (T)**: - We are calculating for \( T = 1 \) year. 4. **Calculate Simple Interest (SI)**: - The formula for Simple Interest is: \[ SI = \frac{P \times R \times T}{100} \] - Substituting the values: \[ SI = \frac{100 \times 5 \times 1}{100} = 5 \text{ rupees} \] 5. **Calculate the Amount for Compound Interest (CI)**: - The formula for the amount when calculating Compound Interest is: \[ A = P \times \left(1 + \frac{R}{100}\right)^T \] - Substituting the values: \[ A = 100 \times \left(1 + \frac{5}{100}\right)^1 = 100 \times 1.05 = 105 \text{ rupees} \] 6. **Calculate Compound Interest (CI)**: - The formula for Compound Interest is: \[ CI = A - P \] - Substituting the values: \[ CI = 105 - 100 = 5 \text{ rupees} \] 7. **Compare Simple Interest and Compound Interest**: - From our calculations: - Simple Interest (SI) = 5 rupees - Compound Interest (CI) = 5 rupees - Therefore, for the first year, Simple Interest and Compound Interest are equal. ### Conclusion: The statement is true: When the interest is calculated annually, Simple Interest and Compound Interest are equal for the first year.
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PEARSON IIT JEE FOUNDATION-SIMPLE INTEREST AND COMPOUND INTEREST -Very Short Answer Type Questions
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