How does the effective interest rate compare with the compound rate on a loan or investment?

Um... it would be really nice to have a context here. The first thing that occurs to me is that you're referring to yield. I can give an example of that and hope that's what you mean.

Let's say you have $1000 and are getting 5% on it compounded quarterly, for one year. That is 1.25% per quarter.

Qtr 1: $1000 interest = $12.50 (1000 x .0125)
When it compounds it means we're adding it on. So we end up with $1012.50 after that.

Qtr 2: $1012.50 interest = $12.66.
Again we add that on and have $1025.16

Qtr 3: $1025.16 interest = $12.81. Added on gives us $1037.97.

Qtr 4: $1037.97 interest = $12.97.
Add on gives us $1050.94

In the end, we have $1050.94.

$1000 x 5% = $50. Compounding it gave us .94 extra. (OK, it's not much, but we're making a point here. ;)) That's what the compounding effect did, because we get interest on the interest already earned.

The yield on this 5.094%. We got 50.94 in interest, on $1000: 50.94/1000 = 5.094%. So we "effectively" got 5.094%. It means we got the equivalent of something else due to the compounding.

I've had daily compounding on a lot of CD's. They tend to quote the annual yield rather than the rate. Like one I just looked at had an annual rate of 4.64% but with the compounding the yield came out to 4.75%.

There are, however, other places where this can be applied.