David can receive one of the following two payment streams:

• 100 at time 0, 200 at time n years, and 300 at time 2n years
• 600 at time 10 years

At an annual effective interest rate of i, the present values of the two streams are equal.

Given 0.76 = vⁿ, calculate i

• 3.5%
• 4.0%
• 4.5%
• 5.0%
• 5.5%

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

Solution: A

Equating present values:

[[math]] \begin{array}{l}{{100+200\nu^{a}+300\nu^{2a}=600\nu^{10}}}\\ {{100+200(0.76)+300(0.76)^{2}=600\nu^{10}}}\\ {{0.7086=\sqrt{0.7}}}\\ {{1.03501=1+i}}\\ {{i=3.5\%.}}\end{array} [[/math]]

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