The difference between compound interest and simple interest on an amount of ₹15,000 for 2 years is ₹96. Find the rate of interest per annum.

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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 interest and simple interest increases with time and interest rate.

Introduction:

Interest is the cost of borrowing money or the return on an investment. Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal amount plus any accumulated interest. The difference between these two methods becomes significant over longer periods and higher interest rates. This question requires us to find the rate of interest given the difference in interest earned over two years on a principal amount of ₹15,000. The approach will be analytical, using mathematical formulas to solve the problem.

Body:

1. Formulas:

  • Simple Interest (SI): SI = (P × R × T) / 100, where P = Principal, R = Rate of interest, T = Time in years.
  • Compound Interest (CI): CI = P (1 + R/100)^T – P

2. Setting up the Equation:

The problem states that the difference between the compound interest (CI) and simple interest (SI) for two years is ₹96. Therefore, we can write the equation:

CI – SI = 96

Substituting the formulas:

P (1 + R/100)² – P – (P × R × T) / 100 = 96

3. Solving for R:

We know P = 15000 and T = 2. Substituting these values into the equation:

15000 (1 + R/100)² – 15000 – (15000 × R × 2) / 100 = 96

Simplifying the equation:

15000 (1 + 2R/100 + R²/10000) – 15000 – 300R = 96

15000 + 300R + 1.5R² – 15000 – 300R = 96

1.5R² = 96

R² = 96 / 1.5 = 64

R = √64 = 8

Therefore, the rate of interest per annum is 8%.

Conclusion:

The rate of interest per annum that results in a difference of ₹96 between compound interest and simple interest on ₹15,000 over two years is 8%. This was determined by formulating an equation based on the definitions of simple and compound interest and solving for the unknown rate. Understanding the difference between simple and compound interest is crucial for making informed financial decisions, whether it’s borrowing money or investing. Financial literacy programs should emphasize the practical application of these concepts to empower individuals to manage their finances effectively and achieve their financial goals. This promotes holistic development and financial well-being within a society.

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