Revision as of 13:26, 19 November 2023 by Admin (Created page with "An investor deposits 1000 at the beginning of each year for 20 years. The fund earns interest at an annual effective rate of 9.25%. At the end of 20 years, the investor wishes to use the fund to purchase a 30-year annuity-due with monthly payments of 500 based on an annual nominal interest rate of 10% convertible monthly. Calculate the balance, if any, in the fund after paying for the annuity. <ul class="mw-excansopts"><li>The fund balance is insufficient to purchase t...")
ABy Admin
Nov 19'23
Exercise
An investor deposits 1000 at the beginning of each year for 20 years. The fund earns interest at an annual effective rate of 9.25%. At the end of 20 years, the investor wishes to use the fund to purchase a 30-year annuity-due with monthly payments of 500 based on an annual nominal interest rate of 10% convertible monthly.
Calculate the balance, if any, in the fund after paying for the annuity.
- The fund balance is insufficient to purchase the annuity.
- 0
- 35
- 370
- 510
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 19'23
Solution: C
[[math]]
\begin{aligned} & 1000 \ddot{s}_{\overline{20} \mid 0.0925}=57,485.26 \\ & 500 \ddot{a}_{\overline{360}| \frac{10}{12} \%}=57,450.21 \\ & 57,485.26-57,450.21=35.05\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.