Find the principal amount, if the compound interest at the rate of 5% per annum, for 3 years is Rs. 1261:

Question

Accepted Answer

To determine the principal amount when the compound interest is Rs. 1261 at a rate of 5% per annum for 3 years, we can use the formula for compound interest:

$$ A = P \left(1 + \frac{r}{100}\right)^n $$

Where:
- $ A $ is the total amount after $ n $ years,
- $ P $ is the principal amount,
- $ r $ is the rate of interest per annum,
- $ n $ is the number of years.

Given:
- Compound Interest (CI) = Rs. 1261
- Rate (r) = 5%
- Time (n) = 3 years

The total amount $ A $ can be expressed as:

$$ A = P + \text{CI} $$

So, $ A = P + 1261 $.

Substituting the values into the compound interest formula:

$$ P + 1261 = P \left(1 + \frac{5}{100}\right)^3 $$

$$ P + 1261 = P \left(1.05\right)^3 $$

$$ P + 1261 = P \times 1.157625 $$

Now, solving for $ P $:

$$ P \times 1.157625 = P + 1261 $$

$$ 1.157625P - P = 1261 $$

$$ 0.157625P = 1261 $$

$$ P = \frac{1261}{0.157625} $$

$$ P \approx 8000 $$

Therefore, the principal amount is approximately Rs. 8000, which corresponds to Option 2.

**Explanation for Other Options:**

1. **Option 1 (Rs. 8500):** If we assume the principal to be Rs. 8500, the compound interest calculated using the formula would not match Rs. 1261. The total amount would be higher, indicating that Rs. 8500 is not the correct principal.

2. **Option 3 (Rs. 7550):** Similarly, using Rs. 7550 as the principal would result in a compound interest amount that is less than Rs. 1261, which means this option is incorrect.

3. **Option 4 (Rs. 7500):** With Rs. 7500 as the principal, the compound interest calculated would also be less than Rs. 1261, making this option incorrect as well.

Thus, the correct principal amount is Rs. 8000, which is Option 2.