Revision as of 21:14, 18 November 2023 by Admin (Created page with "'''Solution: D''' The present value of the first year's payments is: <math display="block"> \begin{aligned} & 1.08^{\frac{1}{12}}-1=0.00643403 \\ & 500 a_{\overline{12} \mid 0.006434}=5756.43 \end{aligned} </math> This perpetuity can be thought of as a geometrically increasing perpetuity-due with first payment 5756.43. The present value is: <math display="block"> \begin{aligned} & 5756.43\left[\frac{1}{0.08-0.05}\right] 1.08 \\ & =207,231.44 \end{aligned} </math>...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: D
The present value of the first year's payments is:
[[math]]
\begin{aligned}
& 1.08^{\frac{1}{12}}-1=0.00643403 \\
& 500 a_{\overline{12} \mid 0.006434}=5756.43
\end{aligned}
[[/math]]
This perpetuity can be thought of as a geometrically increasing perpetuity-due with first payment 5756.43. The present value is:
[[math]]
\begin{aligned}
& 5756.43\left[\frac{1}{0.08-0.05}\right] 1.08 \\
& =207,231.44
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.