For a select and ultimate mortality model with a one-year select period, you are given:

(i) [math]\quad p_{[x]}=(1+k) p_{x}[/math], for some constant [math]k[/math]

(ii) [math]\quad \ddot{a}_{x: n}=21.854[/math]

(iii) [math]\quad \ddot{a}_{[x]: n]}=22.167[/math]

Calculate [math]k[/math].

• 0.005
• 0.010
• 0.015
• 0.020
• 0.025

For a 10-year certain and life annuity-due on (65) with annual payments you are given:

i) Mortality follows the Standard Ultimate Life Table

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

Calculate the probability that the sum of the payments on a non-discounted basis made under the annuity will exceed the expected present value of the annuity at issue.

• 0.826
• 0.836
• 0.846
• 0.856
• 0.866

For a life annuity-due issued to (55), you are given:

i) The annuity pays an annual benefit of [math]X[/math] through age 64

ii) Beginning at age 65 , the annuity pays [math]75 \%[/math] of [math]X[/math]

iii) The present value of this annuity is 250,000

iv) Mortality follows the Standard Ultimate Life Table v) [math]\quad i=0.05[/math]

Calculate [math]X[/math].

• 17,400
• 17,500
• 17,600
• 17,700
• 17,800

For a 3-year temporary life annuity due, you are given:

i) The life annuity pays 10 at the beginning of each year

ii) [math]v=0.93[/math]

iii) [math]\quad p_{x}=0.95, p_{x+1}=0.9, p_{x+2}=0.8[/math]

Calculate the standard deviation of the present value random variable for this annuity.

• 4.4
• 4.5
• 4.6
• 4.7
• 4.8