The difference between compound and simple interest for a certain amount over 3 years at an annual rate of 5% is ₹61. Find the principal amount.

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Points to Remember:

  • Simple interest is calculated only on the principal amount.
  • Compound interest is calculated on the principal amount plus accumulated interest.
  • The difference between compound and simple interest increases with time and interest rate.

Introduction:

This question requires a factual and analytical approach to determine the principal amount based on the given difference between compound and simple interest over three years. Simple interest (SI) is calculated as SI = (P × R × T) / 100, where P is the principal, R is the rate of interest, and T is the time period. Compound interest (CI) is calculated as CI = P(1 + R/100)^T – P. The difference between CI and SI grows exponentially with time and interest rate. We will use the given difference of ₹61 to solve for the principal amount.

Body:

1. Setting up the Equations:

Let P be the principal amount. The simple interest for 3 years at 5% annual rate is:

SI = (P × 5 × 3) / 100 = 0.15P

The compound interest for 3 years at 5% annual rate is:

CI = P(1 + 5/100)^3 – P = P(1.05)^3 – P = P(1.157625 – 1) = 0.157625P

2. Calculating the Difference:

The difference between compound interest and simple interest is given as ₹61:

CI – SI = 61

0.157625P – 0.15P = 61

0.007625P = 61

3. Solving for the Principal (P):

P = 61 / 0.007625

P ≈ 8000

Therefore, the principal amount is approximately ₹8000.

Conclusion:

By setting up and solving equations representing simple and compound interest calculations, we determined that the principal amount is approximately ₹8000. The difference between compound and simple interest arises because compound interest accrues interest on previously earned interest, leading to a larger final amount. This difference becomes more significant over longer time periods and higher interest rates. Understanding the nuances of simple and compound interest is crucial for making informed financial decisions, particularly in areas like investments and loans. Financial literacy programs should emphasize the practical application of these concepts to empower individuals to manage their finances effectively.

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