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

(i) [math]\quad q_{x+15}=0.10[/math]

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

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

(iv) [math]{ }_{t} V[/math] denotes the net premium policy value at time [math]t[/math]

(v) [math]{ }_{16} V=49.78[/math]

Calculate [math]{ }_{15.6} \mathrm{~V}[/math].

• 49.7
• 50.0
• 50.3
• 50.6
• 50.9

For a fully discrete 5-payment whole life insurance of 1000 on (80), you are given:

(i) The gross premium is 130

(ii) [math]\quad q_{80+k}=0.01(k+1), \quad k=0,1,2, . ., 5[/math]

(iii) [math]\quad v=0.95[/math]

(iv) [math]\quad 1000 A_{86}=683[/math]

(v) [math]{ }_{3} L[/math] is the prospective loss random variable at time 3, based on the gross premium

Calculate [math]E\left[{ }_{3} L\right][/math].

• 330
• 350
• 360
• 380
• 390

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

(i) [math]\quad q_{x+10}=0.02067[/math]

(ii) [math]v^{2}=0.90703[/math]

(iii) [math]A_{x+11}=0.52536[/math]

(iv) [math]{ }^{2} A_{x+11}=0.30783[/math]

(v) [math]{ }_{k} L[/math] is the prospective loss random variable at time [math]k[/math]

Calculate [math]\frac{\operatorname{Var}\left({ }_{10} L\right)}{\operatorname{Var}\left({ }_{11} L\right)}[/math].

• 1.006
• 1.010
• 1.014
• 1.018
• 1.022

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

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

(i) Expenses incurred at the beginning of the first year are 300 plus [math]50 \%[/math] of the first year premium

(ii) Renewal expenses, incurred at the beginning of the year, are [math]10 \%[/math] of each of the renewal premiums

(iii) Mortality follows the Standard Ultimate Life Table

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

(v) Gross premiums are calculated using the equivalence principle

Calculate the gross premium policy value for this insurance immediately after the second premium and associated renewal expenses are paid.

• 200
• 340
• 560
• 720
• 1060

For a fully discrete whole life insurance of 1000 on (35), you are given:

(i) First year expenses are [math]30 \%[/math] of the gross premium plus 300

(ii) Renewal expenses are [math]4 \%[/math] of the gross premium plus 30

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

(iv) Gross premiums are calculated using the equivalence principle

(v) The gross premium policy value at the end of the first policy year is [math]R[/math]

(vi) Using the Full Preliminary Term Method, the modified net premium reserve at the end of the first policy year is [math]S[/math]

(vii) Mortality follows the Standard Ultimate Life Table

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

Calculate [math]R-S[/math].

• -280
• -140
• 0
• 140
• 280

A special fully discrete 10 -payment 10 -year deferred whole life annuity-due on (55) of 1000 per year provides for a return of premiums without interest in the event of death within the first 10 years. You are given:

(i) Annual net premiums are level

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) [math]\quad(I A)_{55: 10}^{1}=0.14743[/math]

Calculate [math]{ }_{9} V[/math], the net premium policy value at the end of year 9 .

• 11,540
• 11,650
• 11,760
• 11,870
• 11,980

For two fully discrete whole life insurance policies on [math](x)[/math], you are given:

(i)

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

(iii) The two policies are priced using the same mortality table.

Calculate [math]W[/math].

• 30.8
• 38.5
• 46.2
• 53.9
• 61.6

For a 40 -year endowment insurance of 10,000 issued to (25), you are given:

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

(ii) [math]\quad p_{25}=0.995[/math]

(iii) [math]\quad \ddot{a}_{25: \overline{20}}=11.087[/math]

(iv) [math]\quad \ddot{a}_{25: 40}=16.645[/math]

(v) The annual level net premium is 216

(vi) A modified net premium reserving method is used for this policy, where the valuation premiums are: - A first year premium equal to the first year net cost of insurance, - Level premiums of [math]\beta[/math] for years 2 through 20, and - Level premiums of 216 thereafter.

Calculate [math]\beta[/math].

• 140
• 170
• 200
• 230
• 260

For a fully discrete whole life insurance policy of [math]1,000,000[/math] on (50), you are given:

(i) The annual gross premium, calculated using the equivalence principle, is 11,800

(ii) Mortality follows the Standard Ultimate Life Table

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

Calculate the expense loading, [math]P^{e}[/math], for this policy.

• 480
• 580
• 680
• 780
• 880