PV of par: 1,000 / 1.064^13 = 446.43562, round to 446.44
PV of the coupons = Price - PV of par = 1065 - 446.44 = 618.56
Use PV ordinary annuity to solve for PMT (the coupon)
PVoa = PMT[((1 - (1 / 1+r)^n)) / r]
618.56 = PMT[((1 - (1 / 1.064^13)) / 0.064]
618.56 = PMT[(1 - 0.44644) / 0.064]
618.56 = PMT[8.64944]
PMT = 618.56 / 8.64944
PMT = 71.51443
coupon rate = PMT / par = 71.51443 / 1000 = 0.07151, or 7.151%
note that bond sells at a premium, coupon rate > market rate (YTM)
Lyon Manfucaturing has bonds on the market making annual payments, with 13 years to maturity, and selling for $1,095. At this price, the bonds yield 6.4 percent. What must the coupon rate be on these bonds???
