Revision as of 21:28, 18 November 2023 by Admin (Created page with "The following deposits are made into a fund at the beginning of each year: {| class="table" ! Year !! Deposit |- | 1 || 100 |- | 2 || 100 |- | 3 || 150 |- | 4 || 150 |- | 5 || 150 |} The fund earns an annual effective interest rate of 13%. At the end of the tenth year, the fund is used to purchase a perpetuity-immediate with semiannual payments of X. The perpetuity earns an annual effective interest rate of 12%. Calculate X. <ul class="mw-excansopts"><li>99</li><li>...")
ABy Admin
Nov 18'23
Exercise
The following deposits are made into a fund at the beginning of each year:
| Year | Deposit |
|---|---|
| 1 | 100 |
| 2 | 100 |
| 3 | 150 |
| 4 | 150 |
| 5 | 150 |
The fund earns an annual effective interest rate of 13%. At the end of the tenth year, the fund is used to purchase a perpetuity-immediate with semiannual payments of X. The perpetuity earns an annual effective interest rate of 12%.
Calculate X.
- 99
- 102
- 105
- 180
- 204
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: A
[[math]]
\begin{aligned}
& {\left[100 \ddot{s}_{\overline{5} \mid 0.13}+50 \ddot{s}_{\overline{3} | 0.13}\right](1.13)^5=1703.81} \\
& \frac{x}{1.12^{1 / 2}-1}=1703.81 \\
& X=99.33
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.