A newly issued ten-year option-free bond is valued at par on June 1,2000. The bond has an annual coupon of 8%. On June 1,2003, the bond has a yield to maturity of 7.1%. Assume that the first coupon is reinvested at 8% and the second coupon is reinvested at 7%. The future bond price of the bond on June 1,2003, is closest to: A 100.0% of par B 102.5% of par C 104.8% of par D 105.4% of par Answer: C A three-year option-free bond with an 8 percent annual coupon rate has a yield to maturity of 9 percent. Assume that the one-and two-year spot rates are 6.5 percent and 7.0 percent,respectively. The three-year spot rate is closest to: A 6.4% B 8.1% C 9.0% D 9.2% Answer 
for the secound question , PV=C1/(1+r)+C2(1+r)^2+(C3+fv)/(1+r)^3 so solve for the equation using the spot rates for the right handside and for the left handside the pv calculate as normal by the bonds func or TVM . FV=100 First r = spotrate of one year secound r +spot rate of second year third is the unknown
Hey man for question one you can automatically elminate A because you know that the coupon is greater than the YTM in 2003 so it has to sell at a premium. The 8% and 7 % are irrellavent because those were prior rates that you would reinvest in and you are looking for the PV of the bond in 2003. So plug in these figures I=7.1, N = 7 (10 -3) FV = PAR 100 PMT = 8 PV = 104.83 (premium) Letter C As for your second question its boot strapping. Remember that you need to discount your coupon and bond prive to PV. So you first need to find the present value of your bond. which is PMT = 8, I = 9, FV = 100, N = 3 PV = 97.47 this is the number you need to equate your other side of the equation to which is going to include discounted values of coupons and bond price. 97.47 = 8/1.065 + 8/1.07^2 + 8+100/1+x^3 Subtract your discounted coupons from both sides and you wind up with 82.97 = 108/1+x^3 get your denominator to the other side and after some algebra you get this 108/82.97 = 1+x^3 108/82.97 = 1.30167 = 1+x^3 again after some algebra you get this (1.30167)^.3333=1.0918 - 1 = 9.18 or 9.2% letter D
I learned a trick from the secret sauce for number 2 to do it without any calculation. You need to get an YIELD of 9% but got 6.5% and 7.0% in the first two years. So to get an yield of 9%, your 3rd year spot rate must be greater than 9% and hence 9.2%.