I am not an orthodox New Keynesian macroeconomist (ONKM), but I can pretend to be one.
Q: What determines the rate of interest?
ONKM: "The central bank sets the rate of interest."
Discussion: the above answer is a pure liquidity preference theory of the rate of interest. By having a perfectly elastic money supply curve, at some rate of interest chosen by the central bank, the stock of money adjusts to equal whatever quantity of money is demanded at that rate of interest. Like in all liquidity preference theories, the rate of interest is determined by the demand for money and the supply of money. The only difference here is that the money supply curve is perfectly interest-elastic.
Q: But what determines where the central bank chooses to set the rate of interest?
ONKM: "Loanable funds."