Revision as of 10:53, 18 November 2023 by Admin (Created page with "'''Solution: C''' From the first annuity, <math display = "block"> X = 21.8 s_{\overline{n}|0.109} = 21.8\cdot{\frac{1.109^{n}-1}{0.109}}=200[1.109^{n}-1]. </math> From the second annuity, <math display = "block"> X = 19,208( v^{n}+ v^{2n}+\cdots)=19,208{\frac{ v^{n}}{1- v^{n}}}=19,208{\frac{1}{1.109^{n}-1}} </math> Hence, <math display = "block"> \begin{array}{l}{{200[1.109^{n}-1]=19,208\frac{1}{1.109^{n}-1}}}\\ {{\mathrm{~[1.109^{n}-1]^{2}=19,208/200=96.04}}}\\...")
Exercise
ABy Admin
Nov 18'23
Answer
Solution: C
From the first annuity,
[[math]]
X = 21.8 s_{\overline{n}|0.109} = 21.8\cdot{\frac{1.109^{n}-1}{0.109}}=200[1.109^{n}-1].
[[/math]]
From the second annuity,
[[math]]
X = 19,208( v^{n}+ v^{2n}+\cdots)=19,208{\frac{ v^{n}}{1- v^{n}}}=19,208{\frac{1}{1.109^{n}-1}}
[[/math]]
Hence,
[[math]]
\begin{array}{l}{{200[1.109^{n}-1]=19,208\frac{1}{1.109^{n}-1}}}\\ {{\mathrm{~[1.109^{n}-1]^{2}=19,208/200=96.04}}}\\ {{{ X=200(9.8)=1960.}}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.