Sam deposits 5000 at the beginning of each year for ten years. The deposits earn an annual effective interest rate of i. All interest is reinvested at an annual effective interest rate of 5%. Sam has 100,000 at the end of ten years.

Calculate i.

• 11.6%
• 15.6%
• 19.1%
• 23.2%
• 27.6%

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

Solution: B

[[math]] \begin{array}{c}{{5000(10)+50000i(I s)_{\overline{10}|0.05}=100,000}}\\ {{5000i\left \{ \frac{\ddot{s}_{\overline{10}|0.05}-10}{0.05}\right\}=50,000}}\\ i\left \{ \frac{13.206787-10}{0.05}\right \} = 10\\ {{i=0.15592}} \end{array} [[/math]]

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