Quote from inCom:
Why? Suppose you have 100$ and lose 7% for three consecutive months, as in your example.
Without compounding: 100 - 7 - 7 - 7 = 79$, so you lost 21$.
With compounding: 100 * 0.93 * 0.93 * 0.93 = 80.44$, and you lost just 19.56$.
As another example, suppose instead you won 7% for three months.
Without compounding: 100 + 7 + 7 + 7 = 121$, so you won 21$.
With compounding: 100 * 1.07 * 1.07 * 1.07 = 122.50$, and you won 22.50$, which is more.
In both cases, you're better off by compounding than not.