Question about interest rates and CD's.?

Let's say, I buy a CD that pays 5 percent simple interest each year. I invest $10,000 and at the end of the year I get $10,500 ($10,000 + ($10,000 x 5 percent). Simple enough, this is probably why they call it simple interest.

Now, suppose instead I bought a CD that pays a 5 percent annual rate compounded semiannually, or twice a year. In that case, I would end up with $10,506.25 at the end of the year. Why? Because I earn $250 the first half of the year: $10,000 x 2.5 percent, which is half the 5 percent annual interest rate. And then I earn $256.25 for the second half of the year because I get 2.5 percent on my original $10,000, plus the $250 I earned the first half of the year. In other words, I'm earning compounded interest, a return on my return, so to speak.

My question is why would someone choose the simple interest investment over the compounded semiannual investment or even a quarterly investment plan?

Simple interest can be better sometimes depending on the rate...

If 2 companies had a CD; 1) offered 6.5% simple interest and 2) offered 6% compounded semi-annually.... which one is better?

Well:
1) 6.5% simple--no calculation required

2) 6% is compounded semi-annually. The effective rate is (1.03^2) - 1 = .0609 ; The effective rate being 6.09% (in your case it would be (1.025^2) - 1 = 5.0625%)

So, from the example I gave, simple interest is better... basically, you always compare with equal comparisons(apples to apples)----based on their effective rates

I don't know of any banks that are offering simple interest CDs. Perhaps back in the day, but not now. Is this an academic question, or you've seen these offered?