Revision as of 22:41, 17 November 2023 by Admin (Created page with "An investor wishes to accumulate 5000 in a fund at the end of 15 years. To accomplish this, she plans to make equal deposits of X at the end of each year for the first ten years. The fund earns an annual effective rate of 6% during the first ten years and 5% for the next five years. Calculate X. <ul class="mw-excansopts"><li>224</li><li>284</li><li>297</li><li>312</li><li>379</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 17'23
Exercise
An investor wishes to accumulate 5000 in a fund at the end of 15 years. To accomplish this, she plans to make equal deposits of X at the end of each year for the first ten years. The fund earns an annual effective rate of 6% during the first ten years and 5% for the next five years.
Calculate X.
- 224
- 284
- 297
- 312
- 379
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 17'23
Solution: C
[[math]]
\begin{align*}
5000 = Xs_{\overline{10}|0.06}(1.05)^5 \\
X={\frac{\,5000\,}{13.1808(1.2763)}}=297.22 \\
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.