Matt purchased a 20-year par value bond with semiannual coupons at a nominal annual rate of 6% convertible semiannually at a price of 1722.25. The bond can be called at par value X on any coupon date starting at the end of year 15 after the coupon is paid. The price guarantees that Matt will receive a nominal annual rate of interest convertible semiannually of at least 8%.

Calculate X.

• 1000
• 1059
• 1723
• 1851
• 2148

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.

Solution: E

Since bond rate is less than yield, the bond was bought at a discount. Thus the issuer wishes the coupon payments to continue as long as possible. So we must assume that the bond will be redeemed in 20 years [math]=40[/math] periods. The coupon rate is [math]r=.03[/math] per half year and the yield rate is [math]j=.04[/math] per half year. Thus [math]P=X v_j^{40}+X r a_{\overline{40} \mid}[/math] so

[[math]] \begin{aligned} & 1722.25=X\left(1.04^{-40}+.03 \frac{1-1.04^{-40}}{.04}\right)=X(.2083+.03(19.7928))=X(.8021) \text { so } \\ & X=1722.25 / .8021=2147.18 \end{aligned} [[/math]]

References

Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.