Revision as of 12:03, 18 November 2023 by Admin (Created page with "An investor will accumulate 10,000 at the end of ten years by making level deposits of X at the beginning of each year. The deposits earn 12% simple interest at the end of every year but the interest is reinvested at an annual effective rate of 8%. Calculate X. <ul class="mw-excansopts"><li>508.79</li><li>541.47</li><li>569.84</li><li>597.73</li><li>608.42</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
An investor will accumulate 10,000 at the end of ten years by making level deposits of X at the beginning of each year. The deposits earn 12% simple interest at the end of every year but the interest is reinvested at an annual effective rate of 8%.
Calculate X.
- 508.79
- 541.47
- 569.84
- 597.73
- 608.42
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
The accumulation is
[[math]]
10X+0.12X(Is)_{\overline{10}|0.08}=10X+0.12X{\frac{\ddot{s}_{\overline{10}|0.08}-10}{0.08}}=10X+0.12X{\frac{15.6455-10}{0.08}}=18.4683X
[[/math]]
Then, X = 10,000/18.4683 = 541.47
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.