Understanding Simple Interest: How Long Does It Take to Earn Rs. 81 on Rs. 900 at 4.5% Annual Interest?

Introduction

Simple interest is a method of calculating the interest on a loan or investment. Unlike compound interest, the interest is not added to the account to earn additional interest in subsequent periods. In this article, we will explore how to calculate the time required to earn a specific amount of interest using the formula for simple interest. We will use an example involving Rs. 900 at a 4.5% annual interest rate to demonstrate the process.

Definition of Simple Interest

Simple interest is calculated only on the principal amount, and the same fixed percentage rate is applied to the entire principal for the duration of the loan or investment. The formula for simple interest is:

I PRT/100

where I is the interest, P is the principal, R is the rate of interest per annum, and T is the time in years.

Example: Calculating the Time Required to Earn Rs. 81

Let's consider the scenario where a principal amount of Rs. 900 is invested at an annual interest rate of 4.5%. Our goal is to determine how long it will take to earn Rs. 81 as interest.

Step 1: Understanding the Given Values

Principal (P) Rs. 900 Simple Interest (I) Rs. 81 Rate (R) 4.5% per annum

Step 2: Applying the Simple Interest Formula

To find the time (T) in years, we rearrange the simple interest formula:

T (I x 100) / (P x R)

Substituting the given values:

T  (81 x 100) / (900 x 4.5)T  8100 / 4050T  2 years

This calculation shows that it will take 2 years for Rs. 900 to yield Rs. 81 as interest at an annual interest rate of 4.5%.

Alternative Method for Calculating Annual Interest

Another way to approach the problem is to first determine the annual interest earned and then use it to calculate the time required. Here’s how:

1. Calculate the annual interest:

Interest per year Principal (P) x Rate (R) / 100 Interest per year 900 x 4.5 / 100 40.50

2. Divide the desired interest (Rs. 81) by the annual interest (Rs. 40.50):

Time 81 / 40.50 2 years

This confirms our earlier calculation that it takes 2 years to earn Rs. 81 at an annual interest rate of 4.5% on Rs. 900.

Conclusion

The above steps clearly demonstrate the process of calculating the time required to earn a specific amount of interest using the simple interest formula. By understanding the annual interest and applying basic arithmetic, it is easy to solve such problems accurately.

If you encounter similar questions in your homework or exams, remember to break down the problem and apply the simple interest formula step by step.

Additional Resources

To further enhance your understanding, you can explore additional resources such as online calculators, practice problems, and educational videos focusing on simple and compound interest.