Revision as of 00:39, 19 November 2023 by Admin (Created page with "'''Solution: D''' The annual effective interest rate is 0.08/(1 – 0.08) = 0.08696. <math display = "block"> 500,000/a_{\overline{5}|0.08696}=500,000/3.9205=127,535. </math> This rounds up to 128,000. The equation of value for X is <math display = "block"> \begin{array}{l}{{128,000a_{\overline{{{4}}}|{0.08696}}+X(1.08696)^{-5}=500,000}}\\ {{X=(500,000-417,466.36)(1.51729)=125,227.}}\end{array} </math> {{soacopyright | 2023 }}")
Exercise
ABy Admin
Nov 19'23
Answer
Solution: D
The annual effective interest rate is 0.08/(1 – 0.08) = 0.08696.
[[math]]
500,000/a_{\overline{5}|0.08696}=500,000/3.9205=127,535.
[[/math]]
This rounds up to 128,000. The equation of value for X is
[[math]]
\begin{array}{l}{{128,000a_{\overline{{{4}}}|{0.08696}}+X(1.08696)^{-5}=500,000}}\\ {{X=(500,000-417,466.36)(1.51729)=125,227.}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.