For a special 10 -year deferred whole life annuity-due of 50,000 on (62), you are given:

(i) Level annual net premiums are payable for 10 years

(ii) A death benefit, payable at the end of the year of death, is provided only over the deferral period and is the sum of the net premiums paid without interest

(iii) [math]\quad \ddot{a}_{62}=12.2758[/math]

(iv) [math]\quad \ddot{a}_{62: 10 \mid}=7.4574[/math]

(v) [math]\quad A_{62: 10}^{1}=0.0910[/math]

(vi) [math]\quad \sum_{k=1}^{10} A_{62: k}^{1}=0.4891[/math]

Calculate the net premium for this special annuity.

• 34,400
• 34,500
• 34,600
• 34,700
• 34,800

For a fully discrete 10 -payment whole life insurance of [math]H[/math] on (45), you are given:

(i) Expenses payable at the beginning of each year are as follows:

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) The gross annual premium, calculated using the equivalence principle, is of the form [math]G=g H+f[/math], where [math]g[/math] is the premium rate per 1 of insurance and [math]f[/math] is the per policy fee

Calculate [math]f[/math].

• 42.00
• 44.20
• 46.40
• 48.60
• 50.80

A warranty pays 2000 at the end of the year of the first failure if a washing machine fails within three years of purchase. The warranty is purchased with a single premium, [math]G[/math], paid at the time of purchase of the washing machine.

You are given:

(i) [math]10 \%[/math] of the washing machines that are working at the start of each year fail by the end of that year

(ii) [math]\quad i=0.08[/math]

(iii) The sales commission is [math]35 \%[/math] of [math]G[/math]

(iv) [math]G[/math] is calculated using the equivalence principle

Calculate [math]G[/math].

• 630
• 660
• 690
• 720
• 750

For a fully discrete whole life insurance of 200,000 on (45), you are given:

(i) Mortality follows the Standard Ultimate Life Table.

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

(iii) The annual premium is determined using the equivalence principle.

Calculate the standard deviation of [math]L_{0}[/math], the present value random variable for the loss at issue.

• 25,440
• 30,440
• 35,440
• 40,440
• 45,440

An insurer issues a special 20 payment insurance policy on (45) with the following benefits: - A death benefit of 1000 , payable at the end of year of death, provided death occurs before age 65 ; and - An annuity benefit that pays 2500 at the start of each year, starting at age 65

You are given:

i) Level annual premiums of [math]P[/math] are paid at the beginning of each year

ii) Premiums are calculated based on the equivalence principle

iii) Mortality follows the Standard Ultimate Life Table

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

Calculate [math]P[/math].

• 872
• 896
• 920
• 944
• 968

An insurer issues a fully discrete 20 -year endowment insurance policy of 1,000,000 on (35).

You are given:

i) First year expenses are 55% of the premium plus 150

ii) After the first year, expenses are 5% of the premium plus 50

iii) Mortality follows the Standard Ultimate Life Table

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

v) Premiums are determined using the equivalence principle

Calculate the annual gross premium on this policy.

• 29,000
• 30,000
• 31,000
• 32,000
• 33,000

For a special fully discrete whole life insurance on (40), you are given:

(i) The death benefit is 50,000 in the first 20 years and 100,000 thereafter

(ii) Level net premiums of 875 are payable for 20 years

(iii) Mortality follows the Standard Ultimate Life Table

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

Calculate [math]{ }_{10} V[/math], the net premium policy value at the end of year 10 for this insurance.

• 11,090
• 11,120
• 11,150
• 11,180
• 11,210

A special fully discrete 2 -year endowment insurance with a maturity value of 2000 is issued to (x). The death benefit is 2000 plus the net premium policy value at the end of the year of death. For year 2, the net premium policy value is the net premium policy value just before the maturity benefit is paid.

You are given:

(i) [math]\quad i=0.10[/math]

(ii) [math]\quad q_{x}=0.150[/math] and [math]q_{x+1}=0.165[/math]

Calculate the level annual net premium.

• 1070
• 1110
• 1150
• 1190
• 1230

For a whole life insurance of 1000 with semi-annual premiums on (80), you are given:

(i) A gross premium of 60 is payable every 6 months starting at age 80

(ii) Commissions of [math]10 \%[/math] are paid each time a premium is paid

(iii) Death benefits are paid at the end of the quarter of death

(iv) [math]{ }_{t} V[/math] denotes the gross premium policy value at time [math]t, t \geq 0[/math]

(v) [math]\quad{ }_{10.75} V=753.72[/math]

(vi)

(vii) [math]i^{(4)}=0.08[/math]

Calculate [math]{ }_{10.25} \mathrm{~V}[/math].

• 680
• 690
• 700
• 710
• 730

For a special fully discrete whole life insurance on (40), you are given:

(i) The death benefit is 1000 during the first 11 years and 5000 thereafter

(ii) Expenses, payable at the beginning of the year, are 100 in year 1 and 10 in years 2 and later

(iii) [math]\pi[/math] is the level annual premium, determined using the equivalence principle

(iv) [math]G=1.02 \times \pi[/math] is the level annual gross premium

(v) Mortality follows the Standard Ultimate Life Table

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

(vii) [math]{ }_{11} E_{40}=0.57949[/math]

Calculate the gross premium policy value at the end of year 1 for this insurance.

• -82
• -74
• -66
• -58
• -50