Explanation:

To determine the principle, let's break it down:

- The interest rate is 12% annually, compounded half-yearly.

- This means a 6% interest rate is applied every 6 months.

- The formula for compound interest \(A = P(1 + \frac{r}{n})^{nt}\), where \(r\) is the annual interest rate, \(n\) is the number of times interest is compounded per year, \(t\) is the time in years, and \(A\) is the amount after interest.

- We know interest (A - P) is Rs 1,545 after one year.

Calculate:

$$

1,545 = P\left(1 + \frac{0.12}{2}\right)^2 - P

$$

$$

1,545 = P(1.06)^2 - P = P(1.1236 - 1)

$$

$$

1,545 = P(0.1236)

$$

$$

P = \frac{1,545}{0.1236} \approx 12,500

$$

- So, Option 1: Rs 12,500 is correct.