Revision as of 12:04, 18 November 2023 by Admin (Created page with "An investment of 10,000 produces a series of 30 annual payments. The first payment of X is made one year after the investment is made. Each successive payment decreases by 5 from the previous payment. At an annual effective interest rate of 5%, calculate X. <ul class="mw-excansopts"><li>685</li><li>695</li><li>705</li><li>715</li><li>725</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
An investment of 10,000 produces a series of 30 annual payments. The first payment of X is made one year after the investment is made. Each successive payment decreases by 5 from the previous payment.
At an annual effective interest rate of 5%, calculate X.
- 685
- 695
- 705
- 715
- 725
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
The equation of value is
[[math]]
\begin{aligned}
10,000=(X+5)a_{\overline{{{30}}}|0.05}^{}-5(I a)_{\overline{{{30}}}|0.05}^{} = (X+5)a_{\overline{{{30}}}|0.05}^{} - 5\frac{\ddot{a}_{\overline{30}|0.05}-30v^{30}}{0.05}\\
=(X+5)(15.37245)-5{\frac{6.14107-6.94132}{0.05}}=15.37245X-843.11275 \\
X = (10, 000 843.11275) /15.37245 =705.36
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.