Remains the same since there was no change in the amount of water being displaced. The anchor would displace the same amount whether it is in the boat or in the water.

DECREASES. Short explanation Volume of water displaced in support (in the boat) is greater than the volume of water displaced when it is sitting at the bottom of the lake. It is in essence to do with relative densities. Long explanation Upthrust is equal to weight (=> volume) of water displaced. With anchor in boat, water supports both boat and anchor. With anchor at bottom of lake, the only upthrust required is to support the boat, the total volume displaced being the "upthrust volume" plus the volume displaced by the anchor being in the water. As the anchor is denser than water, it takes greater volume of water to support it's weight as upthrust (i.e. in the boat) than it does displace when it is sitting at the bottom of the lake. For example, 10000N (~1 metric tonne) of water takes up 1m^3, 10000N of metal will be significantly (metals ~10x more dense than water, so say 10 times) less => 0.1m^3 Therefore, to support a 10000N in a boat, an extra 1m^3 of water would be displaced. However, when the metal is dropped to the bottom (out of boat), the volume of water displaced will be exactly the volume of the anchor, so 0.1m^3 Situation 1 - Boat + anchor floating - Boat individually displaces "x" volume of water, Anchor individually displaces 1m^3 . Situation 2 - Boat + Anchor sunk - Boat individually displaces SAME volume of water. Anchor displaces only 0.1m^3 => Water level decreases. As a more extreme example, imagine you had a small sample (say a teaspoon) of neutron star (high density). If you drop it into the water it will displace exactly a teaspoon of water. To support that sitting in a boat would require a ridiculous (talking significant orders of magnitude) displacement of water, well over a teaspoon.