Calculating the Rate of Simple Interest for a Given Amount

Understanding how to calculate the rate of simple interest is an essential skill in financial management. This article will walk you through a typical problem where you are given the principal amount, the amount after interest, and the time period, and you need to find the rate of interest. The problem we will solve involves a principal of Rs. 1200, which amounts to Rs. 1550 in 2.5 years. Let's break it down step by step.

Calculating Simple Interest

Simple interest is calculated using the formula:

S.I. (Simple Interest) (P × R × T) / 100

Problem Restatement:

Amount after interest: Rs. 1550 Principal amount: Rs. 1200 Time period: 2.5 years Interest paid: 1550 - 1200 Rs. 350

Step-by-Step Solution

1. Calculating the Interest Rate using the Simple Interest Formula:

The formula for the rate of interest (R) is given by:

R (100 × I) / (P × T)

Where:

I is the interest amount P is the principal amount T is the time period in years

Substituting the values:

R (100 × 350) / (1200 × 2.5) 11.6667 ≈ 11.67%

2. Alternative Method: Step Calculation

A step-by-step approach can also be taken to solve this problem:

Calculate the annual interest: Interest per year 350 / 2.5 140 Calculate the annual rate of interest: Rate of interest 140 / 1200 0.11667 ≈ 11.67%

3. Direct Calculation:

Another straightforward method to find the rate of interest involves directly substituting the values into the simple interest formula:

S.I. (P × R × T) / 100

350 (1200 × R × 2.5) / 100

35000 3000R

R 35000 / 3000 ≈ 11.67%

Conclusion

Thus, the rate of simple interest that will make Rs. 1200 amount to Rs. 1550 in 2.5 years is approximately 11.67%. This step-by-step approach can be applied to similar problems to determine the rate of interest for any given principal, amount, and time period. Understanding the simple interest formula and these methods is crucial for managing personal and business finances effectively.