A 9% bond with a 1000 par value and coupons payable semi-annually is redeemable at maturity for 1100. At a purchase price of P, the bond yields a nominal annual interest rate of 8%, compounded semiannually, and the present value of the redemption amount is 190.

Determine P.

• 1050
• 1085
• 1120
• 1165
• 1215

References

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

Solution: C

There are [math]2 n[/math] half years at coupon rate .045 per half year and yield rate .04 per half year. [math]1100 v^{2 n}=190[/math] so [math]v^{2 n}=190 / 1100[/math].

[[math]] P=C v^{2 n}+1000(.045) a_{\overline{2 n} \mid .04}=190+45 \frac{1-v^{2 n}}{.04}=190+45 * \frac{1-190 / 1100}{.04}=1120.682 [[/math]]

References

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