A faulty wall clock is known to gain $15$ minutes every $24$ hours. It is synchronized to the correct time at $9$ AM on $11$th July. What will be the correct time to the nearest minute when the clock shows $2$ PM on $15$th July of the same year?

1. $12:45$ PM
2. $12:58$ PM
3. $1:00$ PM
4. $2:00$ PM