Understanding Simple Interest Calculations

This problem asks us to find the initial sum of money, also known as the principal, that was invested. We are given the simple interest rate per annum, the time period for which the money was invested, and the final amount received after the interest was added to the principal.

Given Information:

• Amount (A) = Rs. 942
• Rate of Simple Interest (R) = 9.5% per annum
• Time Period (T) = 6 years

We need to find the Principal (P).

Simple Interest Formula

The formula for calculating simple interest is:

\( \text{Simple Interest (SI)} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \)

Where:

• \( \text{P} \) is the Principal amount
• \( \text{R} \) is the Rate of interest per annum
• \( \text{T} \) is the Time period in years

The Amount (A) received at the end of the time period is the sum of the Principal and the Simple Interest:

\( \text{A} = \text{P} + \text{SI} \)

Calculating the Principal Amount

We can substitute the formula for Simple Interest (SI) into the Amount formula:

\( \text{A} = \text{P} + \frac{\text{P} \times \text{R} \times \text{T}}{100} \)

Now, we can factor out P from the right side:

\( \text{A} = \text{P} \left( 1 + \frac{\text{R} \times \text{T}}{100} \right) \)

To find the Principal (P), we can rearrange the formula:

\( \text{P} = \frac{\text{A}}{1 + \frac{\text{R} \times \text{T}}{100}} \)

Step-by-Step Calculation

Let's plug in the given values into the derived formula for P:

\( \text{P} = \frac{942}{1 + \frac{9.5 \times 6}{100}} \)

First, calculate the product of Rate and Time:

\( 9.5 \times 6 = 57 \)

Now, substitute this back into the formula:

\( \text{P} = \frac{942}{1 + \frac{57}{100}} \)

Convert the fraction to a decimal:

\( \frac{57}{100} = 0.57 \)

Add this to 1 in the denominator:

\( 1 + 0.57 = 1.57 \)

Finally, perform the division to find P:

\( \text{P} = \frac{942}{1.57} \)

\( \text{P} = 600 \)

So, the sum invested initially was Rs. 600.

Conclusion

The principal amount invested at 9.5% simple interest per annum that grew to Rs. 942 in 6 years is Rs. 600.

Revision Table: Simple Interest Components

Additional Information on Simple Interest

Simple interest is a basic and quick method of calculating the interest charge on a loan or investment. It is calculated only on the principal amount, and the interest earned is not added back to the principal to earn further interest. This is unlike compound interest, where interest is added to the principal, and subsequent interest is calculated on the new, larger principal.

Key points about simple interest:

• Interest is fixed for the entire duration based on the initial principal.
• It is commonly used for short-term loans or simple financial transactions.
• The total interest earned over time is directly proportional to the principal, rate, and time.

Understanding simple interest is fundamental to grasping more complex financial concepts.