exercise:04aa3d0cf9

Jan 20'24

Ten years ago [math]\mathrm{J}[/math], then age 25 , purchased a fully discrete 10 -payment whole life policy of 10,000 .

All actuarial calculations for this policy were based on the following:

(i) Mortality follows the Standard Ultimate Life Table

(ii) [math]\quad i=0.05[/math]

(iii) The equivalence principle

In addition:

(i) [math]\quad L_{10}[/math] is the present value of future losses random variable at time 10.

(ii) At the end of policy year 10 , the interest rate used to calculate [math]L_{10}[/math] is changed to [math]0 \%[/math].

Calculate the increase in [math]E\left[L_{10}\right][/math] that results from this change.

Jan 20'24

Answer: E

[math]L_{10}=10,000 A_{35}=965.30[/math]

[math]L_{10}^{*}=10,000[/math]

[math]L_{10}^{*}-L_{10}=10,000-965.30=9034.70[/math]