A six‐year, 5% semiannual‐pay government bond is priced at 97 per 100 of par value. The annual yield‐to‐maturity (stated annual yield based on monthly compounding) is closest to:
Answer is c. 5.532% but I don’t get it. Can someone please help and see what am I missing? I got 5.74% (see below for my working). What am I not doing right? Thanks in advance!
Below are my workings:
I calculate the yield per semiannual period on the semiannual‐pay bond.
N = 12; PMT = $2.5; FV = $100; PV = −$97; CPT I / Y; I / Y = 2.798%
2.798% is multiplied by 2 to determine the stated annual yield (2.798% × 2 = 5.596%).
I then calculate the monthly compounding using (1 + 5.596%/12)^12 = 1.0574 (5.74%)
Step 1: Calculate Effective Semi-Annual-Yield (as you did) =2,798%
Step 2: Calculate a effective monthly rate = 1,02798^(1/6) -1 = 0,0046
Step 3: Calculate STATED rate = 0,0046 x 12 =0,05532
You should first calculate effective monthly yield and than make the stated yield out of it. Stated yield is always period yield x Number of Periods a Year.
I believe the question asks for effective annual yield, using monthly compounding is not relevant. So you just have to do 1.02798^2 -1 = 5.67%.
Thanks Backwardation, I think I get it, it’s asking for the STATED but I went for the compounded one.
Apologies but there’s a typo in my question, the answer is a. not c.
Backwardation got it right.
Even faster way to calc the rate: set P/Y=2 and C/Y=12 and leave all other inputs the same. Prepare to be amazed when you solve for I/Y!
Thanks but I don’t quite follow, which buttons (commands features) are you referring to in the calculator? Could you please elaborate?
2nd I/Y displays P/Y (payments per year): hit 2 and enter. Hit the down arrow to display C/Y (compounding periods per year): hit 12 and enter. 2nd Quit then go about your TVM solve for I/Y.
Woah! lightbulb moment. Thanks!
Thank you all posting question as well as all your answers. I was very confused about the calucation of similar question from my notes. Happy thanksgiving ya’all.