Revision as of 11:56, 18 November 2023 by Admin (Created page with "The present value of a perpetuity-immediate with a first payment of P and successive annual increases of 9 at an annual effective interest rate of 6% is 2600. Calculate P. <ul class="mw-excansopts"><li>5.50</li><li>6.00</li><li>6.50</li><li>7.00</li><li>7.50</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
The present value of a perpetuity-immediate with a first payment of P and successive annual increases of 9 at an annual effective interest rate of 6% is 2600.
Calculate P.
- 5.50
- 6.00
- 6.50
- 7.00
- 7.50
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: B
[[math]]
\begin{aligned}
2600=P a_{\overline{\infty}|0.06}+v9(I a)_{\overline{\infty}|0.06} \\
=P{\frac{1}{0.06}}+{\frac{1}{1.06}}9{\frac{1.06}{0.06^{2}}} \\
{\frac{P}{0.06}}+2500 \\
P = (2600-2500)(0.06) =6
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.