For a special fully discrete 15 -year endowment insurance on (75), you are given:

(i) The death benefit is 1000

(ii) The endowment benefit is the sum of the net premiums paid without interest

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

(iv) [math]\quad A_{75: 15}=0.70[/math]

(v) [math]\quad A_{75: 15 \mid}=0.11[/math]

Calculate the annual net premium.

• 80
• 90
• 100
• 110
• 120

For a whole life insurance of 100,000 on (45) with premiums payable monthly for a period of 20 years, you are given:

(i) The death benefit is paid immediately upon death

(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 monthly net premium.

• 98
• 100
• 102
• 104
• 106

For fully discrete 30 -payment whole life insurance policies on (x), you are given:

(i) The following expenses payable at the beginning of the year:

(ii) [math]\quad \ddot{a}_{x}=15.3926[/math]

(iii) [math]\quad \ddot{a}_{x: 15 \mid}=10.1329[/math]

(iv) [math]\quad \ddot{a}_{x: 30 \mid}=14.0145[/math]

(v) Annual gross premiums are calculated using the equivalence principle

(vi) The annual gross premium is expressed as [math]k F+h[/math], where [math]F[/math] is the death benefit and [math]k[/math] and [math]h[/math] are constants for all [math]F[/math]

Calculate [math]h[/math].

• 30.3
• 35.1
• 39.9
• 44.7
• 49.5

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

(i) [math]\quad L[/math] is the present value of the loss at issue random variable if the premium rate is determined by the equivalence principle

(ii) [math]\quad L^{*}[/math] is the present value of the loss at issue random variable if the premium rate is 0.06

(iii) [math]\delta=0.07[/math]

(iv) [math]\quad \bar{A}_{x}=0.30[/math]

(v) [math]\quad \operatorname{Var}(L)=0.18[/math]

Calculate [math]\operatorname{Var}\left(L^{*}\right)[/math].

• 0.18
• 0.21
• 0.24
• 0.27
• 0.30

For a fully discrete 10 -year deferred whole life annuity-due of 1000 per month on (55), you are given:

(i) The premium, [math]G[/math], will be paid annually at the beginning of each year during the deferral period

(ii) Expenses are expected to be 300 per year for all years, payable at the beginning of the year

(iii) Mortality follows the Standard Ultimate Life Table

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

(v) Using the two-term Woolhouse approximation, the expected loss at issue is -800 Calculate [math]G[/math].

• 12,110
• 12,220
• 12,330
• 12,440
• 12,550

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 special fully continuous whole life insurance on [math](x)[/math], you are given:

(i) Premiums and benefits:

(ii) [math]\quad \mu_{x+t}=0.03, t \geq 0[/math]

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

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

• 10,130
• 10,190
• 10,250
• 10,310
• 10,370

For a fully discrete 5 -payment whole life insurance of 1000 on (40), you are given:

(i) Expenses incurred at the beginning of the first five policy years are as follows:

(ii) No expenses are incurred after Year 5

(iii) Mortality follows the Standard Ultimate Life Table

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

Calculate the gross premium using the equivalence principle.

• 31
• 36
• 41
• 46
• 51

(35) purchases a fully discrete whole life insurance policy of 100,000 .

You are given:

(i) The annual gross premium, calculated using the equivalence principle, is 1770

(ii) The expenses in policy year 1 are [math]50 \%[/math] of premium and 200 per policy

(iii) The expenses in policy years 2 and later are [math]10 \%[/math] of premium and 50 per policy

(iv) All expenses are incurred at the beginning of the policy year

(v) [math]\quad i=0.035[/math]

Calculate [math]\ddot{a}_{35}[/math].

• 20.0
• 20.5
• 21.0
• 21.5
• 22.0

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

(i) The first year expense is [math]10 \%[/math] of the gross annual premium

(ii) Expenses in subsequent years are [math]5 \%[/math] of the gross annual premium

(iii) The gross premium calculated using the equivalence principle is 2.338

(iv) [math]i=0.04[/math]

(v) [math]\quad \ddot{a}_{x}=16.50[/math]

(vi) [math]{ }^{2} A_{x}=0.17[/math]

Calculate the variance of the loss at issue random variable.

• 900
• 1200
• 1500
• 1800
• 2100