You are given the following information about a special fully discrete 2-payment, 2-year term insurance on (80):

(i) Mortality follows the Standard Ultimate Life Table

(ii) [math]\quad i=0.03[/math]

(iii) The death benefit is 1000 plus a return of all premiums paid without interest

(iv) Level premiums are calculated using the equivalence principle

Calculate the net premium for this special insurance.

• 32
• 33
• 34
• 35
• 36

For a fully discrete 10 -year term life insurance policy on [math](x)[/math], you are given:

(i) Death benefits are 100,000 plus the return of all gross premiums paid without interest

(ii) Expenses are [math]50 \%[/math] of the first year's gross premium, [math]5 \%[/math] of renewal gross premiums and 200 per policy expenses each year

(iii) Expenses are payable at the beginning of the year

(iv) [math]A_{x: 10}^{1}=0.17094[/math]

(v) [math]\quad(I A)_{x: 10 \mid}^{1}=0.96728[/math]

(vi) [math]\quad \ddot{a}_{x: 100}=6.8865[/math]

Calculate the gross premium using the equivalence principle.

• 3200
• 3300
• 3400
• 3500
• 3600

S, now age 65 , purchased a 20 -year deferred whole life annuity-due of 1 per year at age 45. You are given:

(i) Equal annual premiums, determined using the equivalence principle, were paid at the beginning of each year during the deferral period

(ii) Mortality at ages 65 and older follows the Standard Ultimate Life Table

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

(iv) [math]\quad Y[/math] is the present value random variable at age 65 for S's annuity benefits

Calculate the probability that [math]Y[/math] is less than the actuarial accumulated value of S's premiums.

• 0.35
• 0.37
• 0.39
• 0.41
• 0.43

For whole life annuities-due of 15 per month on each of 200 lives age 62 with independent future lifetimes, you are given:

(i) [math]\quad i=0.06[/math]

(ii) [math]\quad A_{62}^{(12)}=0.4075[/math] and [math]{ }^{2} A_{62}^{(12)}=0.2105[/math]

(iii) [math]\quad \pi[/math] is the single premium to be paid by each of the 200 lives

(iv) [math]S[/math] is the present value random variable at time 0 of total payments made to the 200 lives

Using the normal approximation, calculate [math]\pi[/math] such that [math]\operatorname{Pr}(200 \pi \gt S)=0.90[/math].

• 1850
• 1860
• 1870
• 1880
• 1890

For a fully discrete whole life insurance of 1000 on (30), you are given:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) The premium is the net premium

Calculate the first year for which the expected present value at issue of that year's premium is less than the expected present value at issue of that year's benefit.

• 21
• 25
• 29
• 33
• 37

For fully discrete whole life insurance policies of 10,000 issued on 600 lives with independent future lifetimes, each age 62 , you are given:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) Expenses of [math]5 \%[/math] of the first year gross premium are incurred at issue

(iv) Expenses of 5 per policy are incurred at the beginning of each policy year

(v) The gross premium is [math]103 \%[/math] of the net premium.

(vi) [math]{ }_{0} L[/math] is the aggregate present value of future loss at issue random variable

Calculate [math]\operatorname{Pr}\left({ }_{0} L\lt40,000\right)[/math], using the normal approximation.

• 0.75
• 0.79
• 0.83
• 0.87
• 0.91

For a special fully discrete 20 -year endowment insurance on (40), you are given:

(i) The only death benefit is the return of annual net premiums accumulated with interest at [math]5 \%[/math] to the end of the year of death

(ii) The endowment benefit is 100,000

(iii) Mortality follows the Standard Ultimate Life Table

(iv) [math]i=0.05[/math]

Calculate the annual net premium.

• 2680
• 2780
• 2880
• 2980
• 3080

For a fully discrete whole life insurance on (60), you are given:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) The expected company expenses, payable at the beginning of the year, are: - 50 in the first year - 10 in years 2 through 10 - 5 in years 11 through 20 - 0 after year 20

Calculate the level annual amount that is actuarially equivalent to the expected company expenses.

• 7.5
• 9.5
• 11.5
• 13.5
• 15.5

For a fully discrete 20 -year term insurance of 100,000 on (50), you are given:

(i) Gross premiums are payable for 10 years

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) Expenses are incurred at the beginning of each year as follows:

(v) Gross premiums are calculated using the equivalence principle

Calculate the gross premium for this insurance.

• 617
• 627
• 637
• 647
• 657

For a fully discrete 3 -year term insurance of 1000 on [math](x)[/math], you are given:

(i) [math]\quad p_{x}=0.975[/math]

(ii) [math]\quad i=0.06[/math]

(iii) The actuarial present value of the death benefit is 152.85

(iv) The annual net premium is 56.05

Calculate [math]p_{x+2}[/math].

• 0.88
• 0.89
• 0.90
• 0.91
• 0.92