The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate.
Using the formula: (1 + Z3)3 = (1 + 1f0)(1 + 1f1)(1 + 1f2)
where Z = spot rate and nfm = the n year rate m periods from today, (1f0 = the 1 year spot rate now).
(1 + Z3)3 = (1.0375) × (1.095) × (1.158)
Z3 = 1.3155601/3 − 1 = 0.095730, or 9.57%
Then, the value of the zero coupon bond = 100 / (1.09573)3 = 76.01, or approximately $76,
or, using a financial calculator, N = 3; I/Y = 9.57; FV = 1,000; PMT = 0; CPT → PV = 76.20 or approximately $76.
