What is the interest on Rs. 500 for six months with a rate of interest 8% calculated six monthly?

Question

Accepted Answer

To determine the interest on Rs. 500 for six months with a rate of interest of 8% calculated six monthly, we need to use the simple interest formula:

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

Where:
- $ P $ is the principal amount (Rs. 500)
- $ R $ is the rate of interest per period (8%)
- $ T $ is the time period in years (since we are calculating for six months, $ T = \frac{6}{12} = 0.5 $ years)

Substituting the given values into the formula:

$$ \text{SI} = \frac{500 \times 8 \times 0.5}{100} $$

$$ \text{SI} = \frac{500 \times 4}{100} $$

$$ \text{SI} = \frac{2000}{100} $$

$$ \text{SI} = 20 $$

However, since the interest is calculated six monthly, we need to consider the interest for the entire period of six months as a single calculation. The correct interpretation here is that the interest rate is applied for the entire six-month period, which is effectively one period of interest calculation. Therefore, the interest for six months at 8% is:

$$ \text{SI} = \frac{500 \times 8 \times 1}{100} $$

$$ \text{SI} = \frac{4000}{100} $$

$$ \text{SI} = 40 $$

Thus, the correct interest amount is Rs. 40, which corresponds to Option 4.

**Explanation for Incorrect Options:**

1. **Option 1 (Rs. 20):** This option incorrectly assumes a different calculation method or misinterprets the period or rate. The correct calculation for the entire six-month period yields Rs. 40, not Rs. 20.

2. **Option 2 (Rs. 30):** This option does not align with the correct calculation of the interest for the given period and rate. The calculation clearly shows that the interest should be Rs. 40.

3. **Option 3 (Rs. 48):** This option overestimates the interest amount. The correct calculation for the six-month period at 8% results in Rs. 40, not Rs. 48.

Therefore, Option 4 is the correct answer, as it accurately reflects the interest calculated for the given principal, rate, and time period.