Explanation:

To find the compound interest on Rs 12,500 in one year at a 12% annual interest rate, with interest being compounded half-yearly, follow these steps:

- The annual interest rate is 12%, so the half-yearly interest rate is 6%.

- The number of compounding periods in one year is 2.

- Use the compound interest formula:

$$A=P{(1+\frac{r}{n})}^{nt}$$

where:

$A$ = the amount after time $t$

$P$ = principal amount (Rs 12,500)

$r$ = annual interest rate (0.12)

$n$ = number of compounding periods per year (2)

$t$ = time (1 year)

- Calculate:

$$A=12500{(1+\frac{0.12}{2})}^2$$

$$A=12500{(1+0.06)}^2$$

$$A=12500\times 1.1236$$

$$A˜14045$$

- The compound interest is:

$$CI=A-P$$

$$CI˜14045-12500$$

$$CI˜1545$$

- Correct Answer: Option 2 – Rs 1,545