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 fully discrete, 5-payment 10 -year term insurance of 200,000 on (30), you are given:

(i) Mortality follows the Standard Ultimate Life Table

(ii) The following expenses are incurred at the beginning of each respective year:

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

(iv) [math]\quad \ddot{a}_{30: 5}=4.5431[/math]

Calculate the annual gross premium using the equivalence principle.

• 150
• 160
• 170
• 180
• 190

For a special fully discrete 10 -year deferred whole life insurance of 100 on (50), you are given:

(i) Premiums are payable annually, at the beginning of each year, only during the deferral period

(ii) For deaths during the deferral period, the benefit is equal to the return of all premiums paid, without interest

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

(iv) [math]\quad \ddot{a}_{50}=17.0[/math]

(v) [math]\quad \ddot{a}_{60}=15.0[/math]

(vi) [math]{ }_{10} E_{50}=0.60[/math]

(vii) [math]\quad(I A)_{50: 101}^{1}=0.15[/math]

Calculate the annual net premium for this insurance.

• 1.3
• 1.6
• 1.9
• 2.2
• 2.5

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

(i) The annual rate of premium is 560

(ii) Mortality follows the Standard Ultimate Life Table

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

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

Calculate the [math]75^{\text {th }}[/math] percentile of the loss at issue random variable for this policy.

• 610
• 630
• 650
• 670
• 690

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: 10}=7.4575[/math]

(v) [math]\quad(I A)_{55: 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

For a special whole life insurance of 100,000 on (40), you are given:

(i) The death benefit is payable at the moment of death

(ii) Level gross premiums are payable monthly for a maximum of 20 years

(iii) Mortality follows the Standard Ultimate Life Table

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

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

(vi) Initial expenses are 200

(vii) Renewal expenses are [math]4 \%[/math] of each premium including the first (viii) Gross premiums are calculated using the equivalence principle Calculate the monthly gross premium.

• 66
• 76
• 86
• 96
• 106

On July 15, 2017, XYZ Corp buys fully discrete whole life insurance policies of 1,000 on each of its 10,000 workers, all age 35 . It uses the death benefits to partially pay the premiums for the following year.

You are given:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) The insurance is priced using the equivalence principle

Calculate XYZ Corp's expected net cash flow from these policies during July 2018.

• -47,000
• -48,000
• -49,000
• -50,000
• -51,000