Calculating Simple Interest Rate Per Annum

This question asks us to find the annual rate of simple interest given the principal amount, the time period, and the total simple interest earned.

Understanding Simple Interest

Simple interest is calculated only on the principal amount. It does not compound, meaning the interest earned in previous periods does not earn interest in subsequent periods. The formula for simple interest is:

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

Where:

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

Identifying the Given Values

From the question, we are given the following information:

• Principal amount (\( \text{P} \)) = Rs. 5,345
• Time period (\( \text{T} \)) = 10 years
• Simple Interest earned (\( \text{SI} \)) = Rs. 2,672.50

We need to find the Rate of Interest (\( \text{R} \)) per annum.

Rearranging the Formula to Find the Rate

To find the rate (\( \text{R} \)), we can rearrange the simple interest formula:

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

Multiply both sides by 100:

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

Divide both sides by \( \text{P} \times \text{T} \):

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

Calculating the Simple Interest Rate

Now, we substitute the given values into the rearranged formula:

\( \text{R} = \frac{2672.50 \times 100}{5345 \times 10} \)

First, calculate the numerator:

\( 2672.50 \times 100 = 267250 \)

Next, calculate the denominator:

\( 5345 \times 10 = 53450 \)

Now, perform the division:

\( \text{R} = \frac{267250}{53450} \)

\( \text{R} = 5 \)

So, the rate of simple interest per annum is 5%.

Verification

Let's verify this rate using the original formula:

\( \text{SI} = \frac{5345 \times 5 \times 10}{100} \)

\( \text{SI} = \frac{5345 \times 50}{100} \)

\( \text{SI} = \frac{267250}{100} \)

\( \text{SI} = 2672.50 \)

This matches the given simple interest, confirming our calculated rate is correct.

Summary of Calculation

The calculated rate of simple interest per annum is 5%.

Revision Table: Simple Interest Concepts

Additional Information: Simple vs. Compound Interest

It's important to distinguish simple interest from compound interest. In compound interest, the interest earned in each period is added to the principal for the next period's calculation. This leads to earning interest on interest, resulting in faster growth of the investment over time compared to simple interest.

• Simple Interest: Interest is constant each period (if P and R are constant).
• Compound Interest: Interest increases each period because the base (principal + accumulated interest) increases.

The question specifically mentions simple interest, so we use the formula \( \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \).