Revision as of 08:43, 18 November 2023 by Admin (Created page with "A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment. The annual effective rate of interest is 8%. Calculate X. <ul class="mw-excansopts"><li>54</li><li>64</li><li>74</li><li>84</li><li>94</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A perpetuity-immediate pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25-year annuity-immediate that will pay X at the end of the first year. Each subsequent annual payment will be 8% greater than the preceding payment. The annual effective rate of interest is 8%.
Calculate X.
- 54
- 64
- 74
- 84
- 94
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: A
The value of the perpetuity after the fifth payment is 100/0.08 = 1250. The equation to solve is
[[math]]
\begin{array}{c}{{1250=X( v+1.08 v^{2}+\cdots+1.08^{24} v^{25})}}\\ {{=X( v+ v+\cdots+ v)=X(25)/1.08}}\\ {{X=50(1.08)=54.}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.