To calculate the conversion factor, we evaluate the hypothetical price of the bond assuming a face value of USD 100, on the first day of the delivery month. First, the maturity is rounded to the nearest 3 months as per the rules in the question. 12 years and 7 months rounded to the nearest 3 months is 12 years and 6 months (12.5 years).

Since it's exactly on a semi-annual coupon date (12.5 years), there are $12.5 \times 2 = 25$semi-annual periods remaining. The bond pays a 6$6\% / 2 = 3\%$ or USD 3 per USD 100 face value. The specified discount rate for calculating the conversion factor is 7% annually, or $7`\% / 2 = 3.5\%$ semi-annually.

Now, calculate the present value (price) of the bond assuming a USD 100 face value: $PV = \sum_{t=1}^{25} \frac{3}{(1 + 0.035)^t} + \frac{100}{(1 + 0.035)^{25}}$ $PV = 3 \times \frac{1 - (1.035)^{-25}}{0.035} + 100 \times (1.035)^{-25}$ $PV = 3 \times 16.4815 + 100 \times 0.423147$ $PV = 49.4445 + 42.3147 = 91.7592$

The conversion factor is the present value divided by the face value: $\text{Conversion Factor} = \frac{91.7592}{100} = 0.9176$