What will be the effect on velocity of money when demand for real money increases? Suppose that a change in government regulations allows banks to start paying 
interest on checking accounts. The money stock is the sum of currency and demand 
deposits, including checking accounts.
(a) How does this change affect the demand for money?
(b) What happens to the velocity of money?
(c) What will happen to the LM curve? 
(d)If the price level is fixed, what will happen to the output and interest rate? Use the 
IS-LM framework to explain your answer.

This was the question given. According to my understanding:
(a) interest on checking accounts means lower cost of holding money so money demand goes up.
(c)Since demand for money has gone up interest rate will go up, hence LM curve shifts to the left.
(d) due to the leftward shift of LM curve interest rate go up and output goes down.
Are my answers correct? How do I insert velocity of money in ISLM model?
(a) The effect of this policy change sounds theoretically ambiguous to me. It ultimately depends on the consumers' preferences. 

An increase in interest payments lowers the opportunity cost of having cash, which might make some consumers better off by saving more and some might see this is a relief and hold more cash. We need an utility function in order to know how consumers would react to the policy change.

(b) Again, ambiguous. It depends on the liquid effect of the policy change on money demand. Let's first remember the Equation of Exchange:

$$MV=PQ$$

If consumers deposit more money on checking accounts, money supply goes up. Given the price level and output are fixed (we're in the short run), an increase in $M$ makes the money velocity $V$ decrease. On the other hand, if consumers deposit less on checking accounts, money supply goes down and velocity of money increases. 

(c) The correct answer - at least in my understanding - is that it's ambiguous. If the money supply increases, the LM shifts to the right and if it decreases, to the left.

(d) If the LM shifts to the right and the price level is fixed, output goes up and interest rates go down, if it shifts to the left, output goes down and interest rates go up.