Calculating the Rate of Interest Using Simple Interest Formulas

Understanding the concept and application of simple interest is essential for anyone dealing with financial matters. This article will guide you through the process of determining the rate of interest based on given principal amounts and time periods. We will explore the formula for simple interest, provide detailed steps, and solve a real-world problem to illustrate the concept.

Understanding Simple Interest

Simple interest is the interest calculated on the principal amount of a loan or deposit for a particular period of time. The formula for simple interest is:

I P × r × t 100

Where:

I is the interest earned (or paid) P is the principal amount (initial amount of money) r is the rate of interest (as a percentage) t is the time period (in years)

In this article, we will apply this formula to solve a problem involving two different time periods and amounts to find the rate of interest.

Solving the Problem

The problem states:

A sum of money at simple interest amounts to Rs. 5700 in 3.5 years and Rs. 6200 in 6 years. What is the rate of interest?

Let's break down the problem into steps:

Step 1: Setting up the Equations

Using the simple interest formula, we can set up two equations:

A P P × r × t 100

For the first scenario:

5700 P P × r × 3.5 100

For the second scenario:

6200 P P × r × 6 100

Let's denote the principal amount as P and the rate of interest as r.

Step 2: Simplifying the Equations

Rearrange both equations to express P in terms of r.

First scenario:

5700 - P P × r × 3.5 100

Second scenario:

6200 - P P × r × 6 100

Eliminate P by subtracting the first equation from the second:

6200 - 5700 P × r × 6 100 - P × r × 3.5 100

500 2.5P r

Solving for r:

r 50000 2.5 P 20000 P

Step 3: Finding the Principal Amount

Substitute r back into one of the original equations to find P.

Using the first equation:

5700 - P P × 20000 P × 3.5 100

Simplify:

5700 - P 20000 × 3.5 100

5700 - P 700

5000 P

Now, substitute P back into the expression for r:

r 20000 5000 4

The rate of interest is 4 per annum.

Conclusion

This problem illustrates the application of the simple interest formula in solving real-world finance problems. By understanding and applying these principles, you can accurately calculate interest rates and manage your finances effectively.