You have decided to invest in Bond X, an n-year bond with semi-annual coupons and the following characteristics:

• Par value is 1000.
• The ratio of the semi-annual coupon rate, r, to the desired semi-annual yield rate, i, is 1.03125.
• The present value of the redemption value is 381.50.

Given [math](1+i)^{-n} = 0.5889[/math], calculate the price of bond X.

• 1019
• 1029
• 1050
• 1055
• 1072

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

Solution: D

Let C be the redemption value and [math]v = 1/(1+i)[/math]. Then

[[math]] \begin{align*} X &= 1000r a_{\overline{2n}|i}+C\nu^{2n}\\ &=1000r\frac{1-\nu^{2n}}{i}+381.50\\ &=10000(1.03125)(1-0.5889^{2})+381.50 \\ &=1055.11 \end{align*} [[/math]]

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