Simple Interest Calculation: Finding the Principal Sum

To find the original sum (principal) that earns a certain simple interest over a period, we can use the simple interest formula and rearrange it.

Given Information:

• Simple Interest (SI) = ₹460
• Time (T) = 4 years
• Rate of Interest (R) = 5% per year

Formula for Simple Interest:

The formula for calculating Simple Interest is:

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

Where:

• SI = Simple Interest
• P = Principal Sum
• R = Rate of Interest (in %)
• T = Time (in years)

Calculating the Principal Sum (P):

We need to find P. We can rearrange the formula:

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

Now, substitute the given values into the rearranged formula:

\(P = \frac{460 \times 100}{5 \times 4}\)

First, calculate the denominator:

\(5 \times 4 = 20\)

Now, calculate the numerator:

\(460 \times 100 = 46000\)

Finally, divide the numerator by the denominator:

\(P = \frac{46000}{20}\)

\(P = 2300\)

Conclusion:

The principal sum required to earn an interest of ₹460 in 4 years at 5% simple interest per year is ₹2300.