A bon will mature in 12 years The bond aenJ o Coaponcade ana

A bon will mature in 12 years. The bond aenJ o Coaponcade ana ? loo o par value and Payi semi annual inle(??.calculate the yield to maduciy Ct) ot the a? annul Cte b) b..ss % c ) J) 2.91 c) 8.48%

Solution

YTM is that discount rate which equates the cash flows from the bond with the price if it is held for 12 year. The cash flows are the maturity value of $1000 at EOY 12 and the semiannual interest of $37.50 for 24 half years. The relevant discount rate has to be found by trial and error. Discounting with 2% (half year rate), PV of the cash flows = = 1000/1.02^24+37.50*(1.02^24-1)/(0.02*1.02^24) = $ 1,330.99 Discounting with 1% (half year rate), PV of the cash flows = = 1000/1.01^24+37.50*(1.01^24-1)/(0.01*1.01^24) = $ 1,584.19 The value of r lies between 1% and 2%. The exact value can be ascertained by simple interpoltaion as below: r = 1+(1584.19-1443.60)/(1584.19-1330.99) = 1.56 % 1.56 % is semi-annual rate; annual rate being = 1.56*2 = 3.11 % Closest option = Option [d] 2.91% All options are wrong. YTM using online calculator 3.06 %