For a special fully discrete whole life insurance policy of 1000 on (90), you are given:

(i) The first year premium is 0

(ii) [math]\quad P[/math] is the renewal premium

(iii) Mortality follows the Standard Ultimate Life Table

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

(v) Premiums are calculated using the equivalence principle

Calculate [math]P[/math].

• 150
• 160
• 170
• 180
• 190

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

For a special fully discrete 2 -year term insurance on [math](x)[/math], you are given:

(i) [math]q_{x}=0.01[/math]

(ii) [math]\quad q_{x+1}=0.02[/math]

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

(iv) The death benefit in the first year is 100,000

(v) Both the benefits and premiums increase by [math]1 \%[/math] in the second year Calculate the annual net premium in the first year.

• 1410
• 1417
• 1424
• 1431
• 1438

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

(i) [math]\quad \mu_{x+t}=0.06[/math], for [math]0 \leq t \leq 3[/math]

(ii) [math]\delta=0.06[/math]

(iii) The annual premium is 315.80

(iv) [math]\quad L_{0}[/math] is the present value random variable for the loss at issue for this insurance Calculate [math]\operatorname{Pr}\left[L_{0}\gt0\right][/math].

• 0.03
• 0.06
• 0.08
• 0.11
• 0.15

For a special 10-year deferred whole life annuity-due of 300 per year issued to (55), you are given:

(i) Annual premiums are payable for 10 years

(ii) If death occurs during the deferral period, all premiums paid are returned without interest at the end of the year of death

(iii) [math]\quad \ddot{a}_{55}=12.2758[/math]

(iv) [math]\quad \ddot{a}_{55: \overline{10}|}=7.4575[/math]

(v) [math]\quad(I A)_{55: \overline{10}|}^{1}=0.51213[/math]

Calculate the level net premium.

• 195
• 198
• 201
• 204
• 208

For a 10 -year deferred whole life annuity-due with payments of 100,000 per year on (70), you are given:

(i) Annual gross premiums of [math]G[/math] are payable for 10 years

(ii) First year expenses are [math]75 \%[/math] of premium

(iii) Renewal expenses for years 2 and later are [math]5 \%[/math] of premium during the premium paying period

(iv) Mortality follows the Standard Ultimate Life Table

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

Calculate [math]G[/math] using the equivalence principle.

• 64,900
• 65,400
• 65,900
• 66,400
• 66,900

For a special fully discrete 5 -year deferred 3 -year term insurance of 100,000 on [math](x)[/math] you are given:

(i) There are two premium payments, each equal to [math]P[/math]. The first is paid at the beginning of the first year and the second is paid at the end of the 5 -year deferral period

(ii) The following probabilities:

(iii) [math]{ }_{5} p_{x}=0.95[/math]

(iv) [math]q_{x+5}=0.02, \quad q_{x+6}=0.03, \quad q_{x+7}=0.04[/math]

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

Calculate [math]P[/math] using the equivalence principle.

• 3195
• 3345
• 3495
• 3645
• 3895

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

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 fully discrete whole life insurance of 1 on [math](x)[/math], you are given:

(i) The net premium policy value at the end of the first year is 0.012

(ii) [math]\quad q_{x}=0.009[/math]

(iii) [math]\quad i=0.04[/math]

Calculate [math]\ddot{a}_{x}[/math].

• 17.1
• 17.6
• 18.1
• 18.6
• 19.1