semi annual vs annual yld

Getting a little beat up by fixed income and can’t make heads/tails of this one: If a 15-year, $1,000 U.S. zero-coupon bond is priced to yield 10%, what is its market price? A) $23.50. B) $239.39. C) $231.38. N = 30; I/Y = 5; PMT = 0; FV = 1,000; CPT ¨ PV = 231.38. Why do we use the semi-annual yield and cpn payments when calculating PV, as opposed to annual inputs? Thanks, John

Market terminology is using Bond Equivalent Yield which is double the semi-annual yield. You need to watch for whether they state annual or semi-annual compounding periods in the question. If they don’t say either, it will more than likely be semi-annual compounding periods.

so semi-annual yld is market convention? i used to work with this stuff so should know, but it’s been a while.

Doubling the semi-annual yield is market convention. If yield is quoted as 5% in the market (unless stated, it should mean with semiannual compounding) , it translates to effective annual yield 5.0625% ((1.025^2)-1). If it has annual compounding, it’s a straight up 5%.

^ very true.

thanks soddy1979, appreciate that