Suppose that all investors expect that interest rates for the 4 years will be as follows: $\begin{array}{lr}
& \text { Forward } \
\text { Year } & \text { Interest Rate } \
\hline 0 & \text { (today) } 6 \% \
1 & 7 \% \
2 & 9 \% \
3 & 10 \%
\end{array}$ What is the yield to maturity of a 3-year zero-coupon bond?
A) 7.03%
B) 9.00%
C) 6.99%
D) 7.49%
E) None of the options are correct.

Question

Quizplus · Accepted Answer

The yield to maturity of a zero-coupon bond is the annual rate of return that equates the present value of the bond's future cash flows to its current price. In this case, the bond has a face value of $1,000 and will mature in 3 years. The present value of the bond's future cash flows is:$$PV = \frac{1000}{(1 + 0.06)^1} + \frac{1000}{(1 + 0.07)^2} + \frac{1000}{(1 + 0.09)^3}$$$$PV = 943.39 + 884.96 + 806.45 = 2634.80$$The current price of the bond is $2,634.80. Therefore, the yield to maturity is:$$YTM = \sqrt[3]{\frac{1000}{2634.80}} - 1 = 6.99%$$

Suppose That All Investors Expect That Interest Rates for the 4