Bonds - Stated Annual Yield Periodicity

CFA Level I Fixed Income
#1

I’m having trouble with a question and I’m hoping that someone can help. The questions are below. I’ve calculated the Semiannual bond basis yield at 6.47%.

  1. A stated annual yield based on annual compounding.
  2. A stated annual yield based on quarterly compounding.
  3. A stated annual yield based on monthly compounding.

These are the formulas given:

(1 + (.0647/2))2 = (1 + (SAY/1))1 = 6.58%

(1 + (.0647/2))2 = (1 + (SAY/4))4 = 6.42%

(1 + (.0647/2))2 = (1 + (SAY/12))12 = 6.38%

I don’t understand these formulas. Is someone able to provide a different formula to help me understand how these stated annual yields are calculated?

#2

I figured it out…I think there were just too many formulas and it was overwhelming LOL