Revision as of 01:07, 18 November 2023 by Admin (Created page with "John deposits 1000 into a fund. The fund earns: # an annual nominal rate of interest of 4% convertible quarterly for the first three years; # a constant annual force of interest of 5% for the next three years; and # an annual nominal discount rate of 6% convertible semiannually thereafter. Calculate the amount in the fund at the end of ten years. <ul class="mw-excansopts"><li>1658</li><li>1667</li><li>1670</li><li>1674</li><li>1677</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
John deposits 1000 into a fund. The fund earns:
- an annual nominal rate of interest of 4% convertible quarterly for the first three years;
- a constant annual force of interest of 5% for the next three years; and
- an annual nominal discount rate of 6% convertible semiannually thereafter.
Calculate the amount in the fund at the end of ten years.
- 1658
- 1667
- 1670
- 1674
- 1677
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
[[math]]
\begin{aligned} & 1000\left(1+\frac{0.04}{4}\right)^{3 \times 4}\left(e^{0.05(3)}\right)\left(1-\frac{0.06}{2}\right)^{-2 \times 4} \\ & =1670.42\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.