A 15-year bond with a face amount of 5000, a redemption value of C, and an annual coupon rate of 7% paid quarterly is purchased at a price that yields an annual nominal rate of 5.6% convertible quarterly.

The amount for amortization of premium in the third coupon payment is 6.88.

Calculate C.

• 5150
• 5165
• 5190
• 5235
• 5275

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

Using the basic formula:

[[math]] \begin{aligned} & B V_2-B V_3=6.88 \\ & \left(87.5 a_{\overline{58} \mid}+C v^{58}\right)-\left(87.5 a_{\overline{57} \mid}+C v^{57}\right)=6.88 \\ & 39.0667-0.00625 C=6.88 \\ & C=5150 \end{aligned} [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.