To calculate the approximate tax proration, we need to determine the number of days from January 1 to August 12.
From January 1 to August 12, there are 223 days (31 days in January + 28 days in February + 31 days in March + 30 days in April + 31 days in May + 30 days in June + 31 days in July + 12 days in August).
Next, we divide the annual property taxes by the number of days in a year (360) to determine the daily tax rate:
$1,743.25 / 360 = $4.84 (rounded to the nearest cent).
Finally, we multiply the daily tax rate by the number of days from January 1 to August 12 to find the approximate tax proration:
$4.84 * 223 = $1,078.32 (rounded to the nearest cent).
Therefore, the approximate tax proration that will be charged to the seller is $1,078.32.