Revision as of 19:42, 18 November 2023 by Admin (Created page with "A perpetuity pays 1 at the beginning of each three-month period. Another perpetuity pays X at the beginning of each four-year period. Using an annual effective interest rate of i, each perpetuity has a present value of 300. Calculate X. <ul class="mw-excansopts"><li>15.41</li><li>15.61</li><li>15.91</li><li>16.21</li><li>16.41</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
A perpetuity pays 1 at the beginning of each three-month period. Another perpetuity pays X at the beginning of each four-year period. Using an annual effective interest rate of i, each perpetuity has a present value of 300.
Calculate X.
- 15.41
- 15.61
- 15.91
- 16.21
- 16.41
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
Let j equal the quarterly rate and let k equal the four-year rate:
[[math]]
\begin{aligned} & 300=\frac{1}{j}(1+j) \\ & j=\frac{1}{299} \\ & \left(1+\frac{1}{299}\right)^4=(1+k)^{\frac{1}{4}} \\ & k=0.054875 \\ & 300=\frac{X(1+k)}{k} \\ & X=15.61\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.