Hey SgtSmackSmitH.

This is done in finance (the concept anyway) where you take limits for the term size to go to zero.

So what you will have to do is adjust S so that the term size goes to zero (so from daily to zero in the limit) and adjust every other quantity that is dependent on this term size (if it is dependent like if the interest rate depends on the term size).

With regards to interest rate, in the limit of continuously compounded interest, this becomes an exponential function in the form of Ae^(rt) to get the value of an asset with initial value A and particular interest characteristics corresponding to r at time t where r and t depend on what units you are you looking at (years/months/days/etc).

If you take the appropriate limit and get either a calculus expression (like a differential equation) or just get a standard result that can be evaluated, then that will be the answer.