For a fully discrete whole life insurance policy of 100,000 on [55], a professional skydiver, you are given:

(i) Level premiums are paid annually

(ii) Mortality follows a 2-year select and ultimate table

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

(iv) The following table of values for [math]A_{[x]+t}[/math] :

Calculate the Full Preliminary Term reserve at time 3.

• 2700
• 3950
• 5200
• 6450
• 7800

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

(i) The death benefit for year [math]k[/math] is [math]25,000 k[/math] plus the net premium policy value at the end of year [math]k[/math], for [math]k=1,2[/math]. For year 2 , this net premium policy value is the net premium policy value just before the maturity benefit is paid

(ii) The maturity benefit is 50,000

(iii) [math]\quad p_{x}=p_{x+1}=0.85[/math]

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

(v) [math]\quad P[/math] is the level annual net premium

Calculate [math]P[/math].

• 27,650
• 27,960
• 28,200
• 28,540
• 28,730

The gross annual premium, [math]G[/math], for a fully discrete 5 -year endowment insurance of 1000 issued on [math](x)[/math] is calculated using the equivalence principle. You are given:

(i) [math]\quad 1000 P_{x: 5 \mid}=187.00[/math]

(ii) The expense policy value at the end of the first year, [math]{ }_{1} V^{e}=-38.70[/math]

(iii) [math]q_{x}=0.008[/math]

(iv) Expenses, payable at the beginning of the year, are:

(v) [math]\quad i=0.03[/math]

Calculate [math]G[/math].

• 200
• 213
• 226
• 239
• 252

For a special fully discrete whole life insurance of 1,000 on (45), you are given:

(i) The net premiums for year [math]k[/math] are:

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) [math]{ }_{20} V[/math], the net premium policy value at the end of the [math]20^{\text {th }}[/math] year, is 0

Calculate [math]W[/math].

• 12
• 16
• 20
• 24
• 28

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

(i) Expenses, incurred at the beginning of each year, equal 30 in the first year and 5 in subsequent years

(ii) The net premium policy value at the end of year 10 is 2290

(iii) Gross premiums are calculated using the equivalence principle

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

(v) [math]\quad \ddot{a}_{x}=14.8[/math]

(vi) [math]\quad \ddot{a}_{x+10}=11.4[/math]

Calculate [math]{ }_{10} V^{g}[/math], the gross premium policy value at the end of year 10.

• 2190
• 2210
• 2230
• 2250
• 2270

Ten years ago [math]\mathrm{J}[/math], then age 25 , purchased a fully discrete 10 -payment whole life policy of 10,000 .

All actuarial calculations for this policy were based on the following:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) The equivalence principle

In addition:

(i) [math]\quad L_{10}[/math] is the present value of future losses random variable at time 10.

(ii) At the end of policy year 10 , the interest rate used to calculate [math]L_{10}[/math] is changed to [math]0 \%[/math].

Calculate the increase in [math]E\left[L_{10}\right][/math] that results from this change.

• 5035
• 6035
• 7035
• 8035
• 9035

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

(i) Expenses, payable at the beginning of the year, are:

(ii) The expense policy value at the end of year 2 is -23.64

(iii) The gross annual premium calculated using the equivalence principle is [math]G=368.05[/math]

(iv) [math]G=1000 P_{x: 3 \mid}+P^{e}[/math], where [math]P^{e}[/math] is the expense loading

Calculate [math]P_{x: 3 \mid}[/math].

• 0.290
• 0.295
• 0.300
• 0.305
• 0.310

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

(i)

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

Calculate the variance of the present value of future loss at [math]t[/math] for Policy B.

• 0.9
• 1.4
• 2.0
• 2.9
• 3.4

For a special semi-continuous 20-year endowment insurance on (70), you are given:

i) The death benefit is 1000

ii) The endowment benefit is 500

iii) Mortality follows the Standard Ultimate Life Table

iv) Deaths are uniformly distributed over each year of age

v) The annual net premium is 35.26

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

Calculate the net premium policy value at the end of year 10 .

• 268
• 272
• 276
• 280
• 284

An insurer issues a 30-year term insurance policy on (40). You are given:

i) Net premiums of 750 are payable quarterly

ii) The death benefit, payable at the end of the quarter of death, is [math]1,000,000[/math]

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

iv) [math]10.5^{V}=10,000[/math] v) [math]q_{50}=0.01[/math]

vi) Mortality is uniformly distributed over each year of age

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

Calculate [math]{ }_{10.75} V[/math].

• 8,360
• 8,370
• 8,380
• 8,390
• 8,400