CFAI Mock Exam Q34

“The one year expected total return is closet to:” A) 4.35% B) 4.5% C) 4.84% In the answer, step four says to calculate the semiannual total return by dividing the total future dollars by the beginning price. (107.525/103)^.5-1 = .02173 Can anyone explain the rational behind the .5. Aren’t they brining it back to PV which is 2 semiannual period? Lastly, the answer is additive, instead of multiplied (1.02173)^2 When are we to calculate one method of additive versus the other method of multiplicative. Thank you!

I think it’s because the formula in the book is for the semiannual return. Then they took the semiannual return and multiplied by 2, which gives you the annual (i think the horizon was one year?) when i did this I just calculated the FV of Cash flows (basically one coupon reinvested for half year, one received at the end of time horizon, plus the price at the time horizon, and added these three up). Then i got my year return (FV/PV)-1. the answer i got wasn’t exactly the same but very close to the right answer, and it happened to be the right answer.