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.

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.