Revision as of 11:45, 18 November 2023 by Admin (Created page with "'''Solution: A''' The present value of the ten level payments is <math>X\ddot{a}_{\overline{\infty}|0.05} = 8.10782X</math>. The present value of the remaining payments is <math display = "block"> \begin{array}{l}{{X\biggl[1+1.05/1.1025+(1.05/1.1025)^{2}+(1.05/1.1025)^{3}+(1.05/1.1025)^{4}+(1.05/1.1025)^{5}\biggr]}}\\ {{=X[1+1.05^{-1}+1.05^{-2}+1.05^{-3}+1.05^{-5}]=X\frac{1-1.05^{-6}}{1-1.05^{-1}}=5.3295X.}}\end{array} </math> Then, 45,000 = 8.10782X + 18.69366X = 2...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: A
The present value of the ten level payments is [math]X\ddot{a}_{\overline{\infty}|0.05} = 8.10782X[/math]. The present value of the remaining payments is
[[math]]
\begin{array}{l}{{X\biggl[1+1.05/1.1025+(1.05/1.1025)^{2}+(1.05/1.1025)^{3}+(1.05/1.1025)^{4}+(1.05/1.1025)^{5}\biggr]}}\\ {{=X[1+1.05^{-1}+1.05^{-2}+1.05^{-3}+1.05^{-5}]=X\frac{1-1.05^{-6}}{1-1.05^{-1}}=5.3295X.}}\end{array}
[[/math]]
Then, 45,000 = 8.10782X + 18.69366X = 26.80148X for X = 1679.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.