Revision as of 20:12, 19 January 2024 by Admin (Created page with "'''Answer: D''' Let <math>k</math> be the policy year, so that the mortality rate during that year is <math>q_{30+k-1}</math>. The objective is to determine the smallest value of <math>k</math> such that <math>v^{k-1}\left({ }_{k-1} p_{30}\right)\left(1000 P_{30}\right) < v^{k}\left({ }_{k-1} p_{30}\right) q_{30+k-1}(1000)</math> <math>P_{30} < v q_{30+k-1}</math> <math>\frac{0.07698}{19.3834}<\frac{q_{29+k}}{1.05}</math> <math>q_{29+k}>0.00417</math> <math>29+k>61...")
Exercise
ABy Admin
Jan 19'24
Answer
Answer: D
Let [math]k[/math] be the policy year, so that the mortality rate during that year is [math]q_{30+k-1}[/math]. The objective is to determine the smallest value of [math]k[/math] such that
[math]v^{k-1}\left({ }_{k-1} p_{30}\right)\left(1000 P_{30}\right) \lt v^{k}\left({ }_{k-1} p_{30}\right) q_{30+k-1}(1000)[/math]
[math]P_{30} \lt v q_{30+k-1}[/math]
[math]\frac{0.07698}{19.3834}\lt\frac{q_{29+k}}{1.05}[/math]
[math]q_{29+k}\gt0.00417[/math]
[math]29+k\gt61 \Rightarrow k\gt32[/math]
Therefore, the smallest value that meets the condition is 33 .
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