A clock shows the time precisely at 4:00 p.m. Calculate the interior angle between the hour hand and the minute hand.

At 4:00 p.m., the minute hand points directly at the 12. We can consider this position as $0^\circ$.

At 4:00 p.m., the hour hand points directly at the 4. A clock face has 12 hours, and a full circle is $360^\circ$. Therefore, each hour mark represents an angle of $\frac{360^\circ}{12} = 30^\circ$.
The angle of the hour hand from the 12 o'clock position (clockwise) is:

The angle between the hour hand and the minute hand is the absolute difference between their positions.

This is the interior angle, as it is less than $180^\circ$.

The interior angle formed between the hour hand and the minute hand at 4:00 p.m. is $\boxed{\text{}120^\circ\text{}}$.