Claire purchases an eight-year callable bond with a 10% annual coupon rate payable semiannually. The bond has a face value of 3000 and a redemption value of 2800. The purchase price assumes the bond is called at the end of the fourth year for 2900, and provides an annual effective yield of 10.0%. Immediately after the first coupon payment is received, the bond is called for 2960. Claire’s annual effective yield rate is i.

Calculate i.

• 9.8%
• 10.1%
• 10.8%
• 11.1%
• 11.8%

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

Solution: C

The semiannual yield rate is

[[math]] 1.1^{1/2}-1 = 0.0488. [[/math]]

Assuming the bond is called for 2900 after four years, the purchase price is

[[math]] 150a_{\overline{8}|0.0488}+2900(1.0488)^{-8}=150(6.4947)+1980.87=2955.08 [[/math]]

With a call after the first coupon, the equation to solve for the semi-annual yield rate (j) and then the annual effective rate (i) is

[[math]] \begin{array}{l}{{2955.08=(150+2960)/(1+j)}}\\ {{1+j=1.05242}}\\ {{i=1.05242^{2}-1=0.10759.}}\end{array} [[/math]]

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