In the realm of financial mathematics, understanding and applying the simple interest formula is a fundamental step in calculating the principal amount needed to accumulate a specific interest over a given time period. This article provides a detailed walkthrough of the process, using a practical example to solve for the principal sum of money that will accumulate to Rs. 5300 at an 8% rate of interest in 9 months.

Understanding Simple Interest

Simple interest is calculated using the formula:

Simple Interest (SI) Principal (P) × Rate (R) × Time (T) / 100

This article will guide you through the steps to solve a problem where you want to find the principal (P) given the simple interest (SI), rate (R), and time (T).

Problem Statement

The problem given is:

What sum of money (principal) will accumulate to Rs. 5300 at an 8% rate of interest in 9 months?

Given Data

Solving the Problem

The formula for simple interest is:

SI (P × R × T) / 100

Substitute the given values:

5300 (P × 8 × 3/4) / 100

Now, simplify the equation step by step:

5300 (P × 8 × 3) / (4 × 100)

5300 (P × 24) / 400

5300 times; 400 P × 24

2,120,000 P × 24

P 2,120,000 / 24

P 88,333.33

Therefore, the sum of money required to accumulate to Rs. 5300 at an 8% rate of interest in 9 months is Rs. 88,333.33.

Alternative Methods and Verification

Let's verify the solution using an alternative method:

Let the sum be Rs. 100.

Interest at 8% for 9 months 100 X 8 X 9/12 / 100 6

If amount is 106, interest is 6/-

If amount is 5300, interest is 5300 X 6 / 106 300

Principal 5300 - 300 Rs. 5000/-

Another method:

Assuming the principal as x:

x × 9/12 × 8/100 5300

Simplifying:

x × 72/1200 5300

x × 6/100 5300

x 530000 / 6

x 50000

This confirms that the principal is Rs. 5000.

Final Answer and Verification

Using the interest formula:

Interest (P × R × T) / 100

Interest (5000 × 8 × 9 / 12) / 100

Interest 5300

Thus, the sum of money required to accumulate Rs. 5300 in 9 months is Rs. 5000.

Conclusion

This article has provided a thorough breakdown of the process to calculate the principal sum of money required to achieve a desired interest over a specific time period using the simple interest formula. The examples provided offer practical methods to verify the accuracy of the solution.

By following these steps, you can ensure that you have a solid understanding of the simple interest calculations used in financial mathematics.