Paul makes one investment of 500 on January 1, 2005 and collects 600 on January 1, 2007 for an annual effective yield of X%. Toby invests 100 on January 1, 2005, invests another 100 on January 1, 2006, and collects an amount Z on January 1, 2007 for an annual effective yield of Y%.

The combination of Paul’s and Toby’s cash flows, produces an annual effective yield of 10%.

Calculate Y% −X%

• 0%
• 1%
• 2%
• 3%
• 4%

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

Solution: C

[[math]] \begin{aligned} & 500(1+X)^2=600 \\ & X=0.095445 \\ & 100(1+Y)^2+100(1+Y)=Z \\ & 600(1.10)^2+100(1.10)=600+Z \\ & Z=236 \\ & 100(1+Y)^2+100(1+Y)=236 \\ & (1+Y)^2+(1+Y)-2.36=0 \\ & (1+Y)=\frac{-1 \pm \sqrt{1+9.44}}{2} \\ & Y=0.115549 \\ & Y-X=0.0201\end{aligned} [[/math]]

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