The total present value of 10,000 now and 10,815 two years from now is the same as the present value of 20,800 one year from now at either of two different annual effective interest rates, x and y.

Calculate the absolute value of the difference between x and y.

• 1.8%
• 2.0%
• 3.0%
• 4.0%
• 5.0%

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

Solution: B

[[math]] \begin{aligned} & 10,000+10,815 v^2=20,800 v \\ & v=\frac{20,800 \pm \sqrt{20,800^2-4(10,815)(10,000)}}{21,630} \\ & v=0.970873 \text { or } 0.952381 \\ & i=0.03 \text { or } 0.05 \\ & |0.03-0.05|=0.02\end{aligned} [[/math]]

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