A 15 year 1000 par bond has 7% semiannual coupons and is callable at par after 10 years. What is the price of the bond to yield 5% nominal semiannual?

• 1000
• 1073
• 1156
• 1467
• 1876

References

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

Solution: C

Since yield is less than the coupon rate, the purchaser paid a premium for the bond. The issuer wants to end the coupon payments as soon as possible. so we assume the bond will be called after 10 years. Take a period to be 6 months. Thus

[[math]]\begin{aligned} P & =C v^{20}+F r a_{\overline{20} \mid}=1000\left(1.025^{20}\right)+35 a_{\overline{20} \mid .025} \\ & =1000\left(1.025^{-20}\right)+35 \frac{1-1.025^{-20}}{.025}=1155.892\end{aligned}[[/math]]

References

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