With compound interest, what happens when you start compounding more and more frequently?

Your money grows faster because the interest is added back into the principle and then the next time it compounds you get interest on the new principle amount.  So for example, you deposit $100 in an account that gets 5% interest compounded semiannually. The first time it compounds you get $5 added to your account so your new balance is $105.  The next time it compounds you get 5% on $105 so you get $5.25 added and so on.  If this is only happening semi-annually that would be all you get for the year.  But if it happens quarterly you would get would get deposits of $5.51 and $5.79 as well.  If it compounds monthly or even daily your money would grow more and more.  Hope this helps.