Jeff has 8000 and would like to purchase a 10,000 bond. In doing so, Jeff takes out a 10 year loan of 2000 from a bank and will make interest-only payments at the end of each month at a nominal rate of 8.0% convertible monthly. He immediately pays 10,000 for a 10-year bond with a par value of 10,000 and 9.0% coupons paid monthly.

Calculate the annual effective yield rate that Jeff will realize on his 8000 over the 10-year period.

• 9.30%
• 9.65%
• 10.00%
• 10.35%
• 10.70%

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

Solution: B

Jeff’s monthly cash flows are coupons of 10,000(0.09)/12 = 75 less loan payments of 2000(0.08)/12 = 13.33 for a net income of 61.67. At the end of the ten years (in addition to the 61.67) he receives 10,000 for the bond less a 2,000 loan repayment. The equation is

[[math]] \begin{align*} 8000=61.67a_{\overline{120}|i^{(12)}/12}+8000(1+i^{(12)}/12)^{-120} \\ i^{(12)/12} = 0.00770875 \\ i =1.00770875^{12}-1=0.0965=9.65\%. \end{align*} [[/math]]

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