Explanation:

To find the amount on compound interest compounded half-yearly, follow these steps:

- Principal (P): Rs. 7,500

- Rate (R): 8% per annum, so 4% per half-year

- Time (T): 1.5 years, which equals 3 half-year periods

Formula for Compound Interest:

$$A=P{(1+\frac{R}{100})}^N$$

- Plug in the values:

$$A=7500{(1+\frac{4}{100})}^3$$

- Simplify:

$$A=7500{\left(1.04\right)}^3$$

$$A=7500\times 1.124864$$

$$A=8436.48$$

- So, the amount after 1.5 years will be Rs. 8,436.48

- This matches Option: 1.

- Correct Option: Option: 1 - Rs. 8,436.48