Resting membrane potential: K+ concentrations and charges on inside and outside of the neuron
Why is the interior negative despite the fact that there are more K+ ions inside than outside, and (2) What exactly causes the net negative charge?


It's because K+ isn't the only player in the game. Yes, there is a bigger concentration of K+ inside of the cell, however, there is also a higher concentration of Na+ outside of the cell, and also, there are other charged ions, such as Cl- or proteins.

One of the main reasons for the gradient is Na+/K+ ATPase, which transports 2 K+ ions to the inside of the cell, while 3 Na+ ions are pumped to the exterior of the cell. This generally yields in a higher concentration of + charge on the outside of the cell.  

The final membrane potential depends on the permeability of the membrane to these ions. Higher the permeability for an ion, the closer is the actual potential to the equilibrium potential of this ion. (you can read about its calculation here.). Since the membrane in a normal state is not permeable to Na+ to a big extent, but is permeable to K+, the resting potential is similar to the equilibrium potential for K+, which is negative (the actual value depends on the specific cell type, generally we can say -70mV in neurons). (The K+ is driven to exit the cell because of the chemical and electrical gradient, which results in negative charge inside of the cell). The approximation of final potential can be calculated by using Goldman equation.

The principle is therefore in selective opening and closing of specific ion channels and functioning of transmembrane pumps.