For a fully continuous whole life insurance policy of 100,000 on (35), you are given:

(i) The density function of the future lifetime of a newborn:

(ii) [math]\delta=0.05[/math]

(iii) [math]\quad \bar{A}_{70}=0.51791[/math]

Calculate the annual net premium rate for this policy.

• 1000
• 1110
• 1220
• 1330
• 1440

For a whole life insurance of 100,000 on [math](x)[/math], you are given:

(i) Death benefits are payable at the moment of death

(ii) Deaths are uniformly distributed over each year of age

(iii) Premiums are payable monthly

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

(v) [math]\quad \ddot{a}_{x}=9.19[/math]

Calculate the monthly net premium.

• 530
• 540
• 550
• 560
• 570

An insurance company sells 15 -year pure endowments of 10,000 to 500 lives, each age [math]x[/math], with independent future lifetimes. The single premium for each pure endowment is determined by the equivalence principle.

(i) You are given:

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

(iii) [math]\quad \mu_{x}(t)=0.02 t, \quad t \geq 0[/math]

(iv) [math]{ }_{0} L[/math] is the aggregate loss at issue random variable for these pure endowments.

Using the normal approximation without continuity correction, calculate [math]\operatorname{Pr}\left({ }_{0} L\gt50,000\right)[/math].

• 0.08
• 0.13
• 0.18
• 0.23
• 0.28

For a fully discrete whole life insurance policy on (61), you are given:

(i) The annual gross premium using the equivalence principle is 500

(ii) Initial expenses, incurred at policy issue, are [math]15 \%[/math] of the premium

(iii) Renewal expenses, incurred at the beginning of each year after the first, are [math]3 \%[/math] of the premium

(iv) Mortality follows the Standard Ultimate Life Table

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

Calculate the amount of the death benefit.

• 23,300
• 23,400
• 23,500
• 23,600
• 23,700

For a fully discrete whole life insurance policy of 100,000 on (35), you are given:

(i) First year commissions are [math]19 \%[/math] of the annual gross premium

(ii) Renewal year commissions are [math]4 \%[/math] of the annual gross premium

(iii) Mortality follows the Standard Ultimate Life Table

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

Calculate the annual gross premium for this policy using the equivalence principle.

• 410
• 450
• 490
• 530
• 570

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

(i) Gross premiums, calculated using the equivalence principle, are payable at an annual rate of 4500

(ii) Expenses at an annual rate of [math]R[/math] are payable continuously throughout the life of the policy

(iii) [math]\quad \mu_{50+t}=0.04[/math], for [math]t\gt0[/math]

(iv) [math]\delta=0.08[/math]

Calculate [math]R[/math].

• 400
• 500
• 600
• 700
• 800

For a fully discrete whole life insurance policy of 50,000 on (35), with premiums payable for a maximum of 10 years, you are given:

(i) Expenses of 100 are payable at the end of each year including the year of death

(ii) Mortality follows the Standard Ultimate Life Table

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

Calculate the annual gross premium using the equivalence principle.

• 790
• 800
• 810
• 820
• 830

For an [math]n[/math]-year endowment insurance of 1000 on ( [math]x[/math] ), you are given:

(i) Death benefits are payable at the moment of death

(ii) Premiums are payable annually at the beginning of each year

(iii) Deaths are uniformly distributed over each year of age

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

(v) [math]{ }_{n} E_{x}=0.172[/math]

(vi) [math]\quad \bar{A}_{x: n}=0.192[/math]

Calculate the annual net premium for this insurance.

• 10.1
• 11.3
• 12.5
• 13.7
• 14.9

XYZ Insurance writes 10,000 fully discrete whole life insurance policies of 1000 on lives age 40 and an additional 10,000 fully discrete whole life policies of 1000 on lives age 80 . [math]\mathrm{XYZ}[/math] used the following assumptions to determine the net premiums for these policies:

(i) Mortality follows the Standard Ultimate Life Table

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

During the first ten years, mortality did follow the Standard Ultimate Life Table.

Calculate the average net premium per policy in force received at the beginning of the eleventh year.

• 29
• 32
• 35
• 38
• 41

For a special fully discrete whole life insurance, you are given:

(i) The death benefit is [math]1000(1.03)^{k}[/math] for death in policy year [math]k[/math], for [math]k=1,2,3 \ldots[/math]

(ii) [math]\quad q_{x}=0.05[/math]

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

(iv) [math]\quad \ddot{a}_{x+1}=7.00[/math]

(v) The annual net premium for this insurance at issue age [math]x[/math] is 110

Calculate the annual net premium for this insurance at issue age [math]x+1[/math].

• 110
• 112
• 116
• 120
• 122