Bond question!!!

3 years ago,an investor purchased a 1000 face ,4.5% semiannual coupon bond with 7 years to maturity priced to yield 6.5% for 888.94, waht is the reinvestment income that must be generated over the life of the bond for the investor to realize a yield of 6.5% ? what i am confused is that if we want to gain 6.5% in return then we need to reinvest in 6.5% and then its the same as YTM, but what i got for YTM was not 6.5%? i am lost now, can someone please explain for me??? thanks,

Are you accounting for the fact that the bond makes semi-annual coupon payments and that the semi annual payment would be 22.50 and the semi-annual YTM would be 3.25%?

isn’t 4.5% a semi-annual coupon rate already??? that’s what i was confused too… so it will be always in annual basis??? thanks for your help…!!!

No, when it’s stated that it pays 4.5% semi-annual coupon, that just means that the total annual payment is 4.5%, but actually paid on a semi-annual basis, or half of 4.5%, twice per year. Luckily, I never got confused with this fact, because I can now see how you would not get this, the wording is not intuitive to say the least. Hopefully, I don’t remember this and get confused on the test!

If that’s the question from Book 6 test 1 then they’re asking for $ not % .065/2=.0325 888.94(1+.0325)^14= $1,391.02 ending value to obtain YTM 6.50 1,391.02 - 1,000.00 Face=391.02 391.02 - 315.00 (total coupons) = 76.02 76.02 reinvestment income generated over life of bond to realize 6.5 yield.