Calculating Simple Interest Time

This problem asks us to find the duration required for an investment to grow from a starting amount to a final amount at a fixed annual simple interest rate.

Understanding the Variables

We are given the following information:

• Principal Amount (P): The initial amount of money invested, which is ₹1,500.
• Final Amount (A): The total amount after the interest is added, which is ₹2,040.
• Rate of Interest (R): The annual interest rate, which is 8% per annum.
• Time (T): The duration for which the money is invested, which we need to calculate.

Step 1: Calculate the Simple Interest Earned

The Simple Interest (SI) is the difference between the final amount and the principal amount.

The formula is: \(SI = A - P\)

Substituting the given values:

\(SI = ₹2,040 - ₹1,500\)

\(SI = ₹540\)

So, the total simple interest earned over the period is ₹540.

Step 2: Use the Simple Interest Formula to Find Time

The formula for Simple Interest is:

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

We need to find the time (T). We can rearrange the formula to solve for T:

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

Step 3: Substitute Values and Calculate Time

Now, we plug the values of SI, P, and R into the rearranged formula:

\(T = \frac{540 \times 100}{1500 \times 8}\)

First, calculate the numerator: \(540 \times 100 = 54000\)

Next, calculate the denominator: \(1500 \times 8 = 12000\)

Now, divide the numerator by the denominator:

\(T = \frac{54000}{12000}\)

Simplify the fraction:

\(T = \frac{54}{12}\)

Divide 54 by 12:

\(T = 4.5\) years

This can also be expressed as a mixed fraction: \(4 \frac{1}{2}\) years.

Conclusion

It will take \(4 \frac{1}{2}\) years for ₹1,500 to become ₹2,040 at a simple interest rate of 8% per annum.