When given an annual rate, say 8 percent as asked to convert it into a semi annual rate, when do you divide the annual rate by 2 (Like a BEY)… ex 8/2 = 4 and when do you use compounding ex. (1+0.8)^0.5

Pay attention to the compounding if compounding is semiannual but rate is annual, you can get the 6 months rate by diving the annual rate by 2. But, if compounding is annual, you have to convert that to the semi annual compounding as you mentioned in the formula and get the rate. Hope this helps!

This is true only in case of semi annual compounding though. I have bee having trouble with other compounding like quarterly and monthly.