Revision as of 11:47, 18 November 2023 by Admin (Created page with "A family purchases a perpetuity-immediate that provides annual payments that decrease by 0.4% each year. The price of the perpetuity is 10,000 at an annual force of interest of 0.06. Calculate the amount of the perpetuity’s first payment. <ul class="mw-excansopts"><li>604</li><li>620</li><li>640</li><li>658</li><li>678</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A family purchases a perpetuity-immediate that provides annual payments that decrease by 0.4% each year. The price of the perpetuity is 10,000 at an annual force of interest of 0.06.
Calculate the amount of the perpetuity’s first payment.
- 604
- 620
- 640
- 658
- 678
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: D
The equation of value is
[[math]]
10.000=X( v+ v^{2}0.996+ v^{3}0.996^{2}+\cdots)=X{\frac{e^{-0.06}}{1- v0.996}}=X{\frac{ v}{1-e^{-0.06}0.996}}=15.189X.
[[/math]]
The solution is X = 10,000/15.189 = 658.37.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.