Revision as of 08:47, 18 November 2023 by Admin (Created page with "To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years. The annual effective rate of interest is i. You are given <math>(1+i)^n = 2.0</math> Calculate i. <ul class="mw-excansopts"><li>11.25%</li><li>11.75%</li><li>12.25%</li><li>12.75%</li><li>13.25%</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of each of the next 2n years.
The annual effective rate of interest is i. You are given [math](1+i)^n = 2.0[/math]
Calculate i.
- 11.25%
- 11.75%
- 12.25%
- 12.75%
- 13.25%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
The equation of value is
[[math]]
\begin{align*}
98S_{\overline{{{3n}}}|}+98S_{\overline{{{2n}}}|}&=8000 \\
\frac{(1+i)^{3n}-1}{i}+\frac{(1+i)^{2n}-1}{i}&=81.63 \\
(1+i)^{n}&=2\\
\frac{8-1}{i}+\frac{4-1}{i} &= 81.63 \\
\frac{10}{i} &= 81.63 \\
i &= 12.25\%
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.