Understanding the Simple Interest Problem

This problem asks us to find the rate of simple interest per annum given a principal amount, the final amount after a certain time period, and the time period itself.

Identifying the Given Values

Let's break down the information provided in the question:

• Principal amount (P) = Rs. 2000
• Amount after 12 months (A) = Rs. 2400
• Time period (T) = 12 months

Calculating the Simple Interest Earned

Simple interest (I) is the difference between the final amount and the principal amount. The formula is:

\( I = A - P \)

Substituting the given values:

\( I = 2400 - 2000 \)

\( I = 400 \)

So, the simple interest earned is Rs. 400.

Converting Time to Years

The time period is given as 12 months. To use the simple interest formula for a rate per annum, the time must be in years. 12 months is equal to 1 year.

\( T = 12 \text{ months} = 1 \text{ year} \)

Applying the Simple Interest Formula to Find the Rate

The formula for simple interest is:

\( I = \frac{P \times R \times T}{100} \)

Where:

• I = Simple Interest
• P = Principal amount
• R = Rate of interest per annum
• T = Time period in years

We need to find R. We can rearrange the formula to solve for R:

\( R = \frac{I \times 100}{P \times T} \)

Now, we substitute the values we have:

• I = 400
• P = 2000
• T = 1

\( R = \frac{400 \times 100}{2000 \times 1} \)

\( R = \frac{40000}{2000} \)

To simplify, we can cancel out zeros:

\( R = \frac{400}{20} \)

\( R = \frac{40}{2} \)

\( R = 20 \)

The rate of simple interest is 20% per annum.

Conclusion

A sum of Rs. 2000 becomes Rs. 2400 in 12 months at a simple interest rate of 20% per annum.

Revision Table: Simple Interest Calculations

Reviewing the key concepts involved in simple interest problems:

• Simple Interest (I) is calculated only on the initial principal amount.
• The formula I = (P × R × T) / 100 is fundamental.
• Ensure time (T) and rate (R) are for compatible periods (e.g., years for both).

Additional Information: Simple vs. Compound Interest

It's important to distinguish simple interest from compound interest:

• Simple Interest: Interest is calculated only on the principal amount. The interest earned each period is the same.
• Compound Interest: Interest is calculated on the principal amount plus any accumulated interest from previous periods. The interest earned grows over time.

This question specifically dealt with simple interest, making the calculation straightforward based on the initial principal.