Assuming semiannual compounding what is the price of a zero

Assuming semiannual compounding, what is the price of a zero coupon bond with 5 years to maturity paying $1,000 at maturity if the YTM is (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Price of the Bond a. 3 percent b. 8 percent c. 13 percent

Solution

Price of bond is the present value of cash flow from bond. As it is zero coupon bonds, it does not pay coupon interest and cash flow is only the maturity value. Price of Bond a. 3 percent $ 861.67 b. 8 percent $ 675.56 c. 13 percent $ 532.73 Working: a. Present value of 1 = (1+i)^-n Where, = (1+0.015)^-10 i 3%/2 = 0.015 = 0.861667 n 5*2 = 10 Present value of maturity value = Maturity Value x Present Value of 1 = $       1,000 x 0.861667 = $     861.67 b. Present value of 1 = (1+i)^-n Where, = (1+0.04)^-10 i 8%/2 = 0.04 = 0.675564 n 5*2 = 10 Present value of maturity value = Maturity Value x Present Value of 1 = $       1,000 x 0.675564 = $     675.56 c. Present value of 1 = (1+i)^-n Where, = (1+0.065)^-10 i 13%/2 = 0.065 = 0.532726 n 5*2 = 10 Present value of maturity value = Maturity Value x Present Value of 1 = $       1,000 x 0.532726 = $     532.73