Bill buys a 10-year 1000 par value bond with semi-annual coupons paid at an annual rate of 6%. The price assumes an annual nominal yield of 6%, compounded semi-annually. As Bill receives each coupon payment, he immediately puts the money into an account earning interest at an annual effective rate of i. At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value of the bond, Bill has earned an annual effective yield of 7% on his investment in the bond.

Calculate i.

• 9.50%
• 9.75%
• 10.00%
• 10.25%
• 10.50%

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

Solution: B

Because the yield rate equals the coupon rate, Bill paid 1000 for the bond. In return he receives 30 every six months, which accumulates to [math]30 s_{\overline{20}| j}[/math] where [math]j[/math] is the semi-annual interest rate. The equation of value is

[[math]]1000(1.07)^{10}=30s_{\overline{20}\vert j}+1000\Longrightarrow s_{\overline{{{20}}}\vert j}=32.238. [[/math]]

Using a calculator to solve for the interest rate produces [math]j=0.0476[/math] and so [math]i = 1.0476^2 - 1 = 0.0975.[/math]

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