Revision as of 09:00, 18 November 2023 by Admin (Created page with "The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i. Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01. Calculate R. <ul class="mw-excansopts"><li>1.23</li><li>1.56</li><li>1.60</li><li>1.74</li><li>1.94</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i. Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.
Calculate R.
- 1.23
- 1.56
- 1.60
- 1.74
- 1.94
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: D
For the first perpetuity,
[[math]]
\begin{align*}
\frac{1}{\left(1+\dot{l}\right)^{2}-1}+1 &= 7.21 \\
\frac{1}{6.21} &= \left(1+i\right)^{2}-1 \\
i &= 0.0775
\end{align*}
[[/math]]
For the second perpetuity,
[[math]]
\begin{align*}
R\left[\frac{1}{\left(1.0775+0.01\right)^{3}-1}+1\right]\left(1.0875\right)^{-1}=7.21 \\
1.286139 R = 7.21(1.0875) 0.286139\\
R=1.74
\end{align*}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.