Revision as of 22:11, 17 November 2023 by Admin (Created page with "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 = v<sup>n</sup>, calculate i <ul class="mw-excansopts"><li>3.5%</li><li>4.0%</li><li>4.5%</li><li>5.0%</li><li>5.5%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 17'23
Exercise
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.
ABy Admin
Nov 17'23
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.