The yield to maturity of a $1,000 bond with a 6.6% coupon rate, semi-annual coupons and two years to maturity is 8.?% APR, compounded semi-annually. What must its price he? Number ofcaupon payments {n}: n = 2 x 2 = 4- 601111011 Rate x Face Value \" I]. 066 x 1.01.10 .. Number of Coupon Payments per Year _ 2 _ APR II]. 087' Per-period yield fr): 1" z w n w = 4. 35% Per-period coupon payment {C}: [I = $33 Face value (FF): FV = $1, +$ 1,000 -$P +533 +533 +533 +533 IIIIlF t= t= 1 12:2 t=3 t=4 961 1 W _ 33 1 1 man \"6220 'F _(1+r)" +(1+r)"0.435 '(1+u.n435)4+(1+u.n435)*' ' A bond with 10 years to maturity has a 6.5 percent semi-annual coupon (that is, the bond pays a $32.5 coupon every six months). Another bond of equal risk and maturity pays has a yield that could be expressed as 11% p.a. compounded monthly. What is the price of the semi-annual bond? Again, the trick here is that you are NOT given the correct yield to maturity for pricing the semi-annual bond: ' We are only given an APR of 11% p.a. with monthly compounding. - By dividing the APR by 12 we will have the MONTHLY PERlOD RATE which is not the correct rate for the semi-annual coupon bond. ' Because the semi-annual bond pays $32.5 coupons every six months we need the SEMI-ANNUAL PERIODIC RATE} There are a number of ways to find the semi-annual periodic rate: 1. Convert APR with monthly compounding to EAR then EAR to APR with semi-annual compounding: r m 0.11 12 rm = (1 + W) 1 = (1 + Ti") - 1 = 11.115719 or 11.571911, 3:. a.with annual compounding T 1 1 rsm_mm = m = (1 + 11,-\")? 1 = (1 + 0.1151191 1 = 5.521593%