(50) just had surgery to remove a life-threatening tumor and is purchasing a 3 -year term life insurance policy with a face amount of 100,000. You are given:

i) The probability of (50) surviving the first year after surgery is [math]55 \%[/math] of the Standard Ultimate Life Table survival probability

ii) If (50) survives the first year, subsequent mortality follows the Standard Ultimate Life Table

iii) Benefits are payable at the end of the year of death

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

Calculate the expected present value of the death benefit.

• 43,000
• 44,000
• 45,000
• 46,000
• 47,000

For three fully discrete insurance products on the same [math](x)[/math], you are given:

(i) [math]\quad Z_{1}[/math] is the present value random variable for a 20 -year term insurance of 50

(ii) [math]\quad Z_{2}[/math] is the present value random variable for a 20 -year deferred whole life insurance of 100

(iii) [math]\quad Z_{3}[/math] is the present value random variable for a whole life insurance of 100 .

(iv) [math]E\left[Z_{1}\right]=1.65[/math] and [math]E\left[Z_{2}\right]=10.75[/math]

(v) [math]\operatorname{Var}\left(Z_{1}\right)=46.75[/math] and [math]\operatorname{Var}\left(Z_{2}\right)=50.78[/math]

Calculate [math]\operatorname{Var}\left(Z_{3}\right)[/math].

• 62
• 109
• 167
• 202
• 238

You are given:

(i) [math]\delta_{t}=0.06, \quad t \geq 0[/math]

(ii) [math]\quad \mu_{x}(t)=0.01, \quad t \geq 0[/math]

(iii) [math]\quad Y[/math] is the present value random variable for a continuous annuity of 1 per year, payable for the lifetime of [math](x)[/math] with 10 years certain

Calculate [math]\operatorname{Pr}(Y\gt\mathrm{E}[Y])[/math].

• 0.705
• 0.710
• 0.715
• 0.720
• 0.725

You are given:

(i) [math]\quad A_{x}=0.30[/math]

(ii) [math]\quad A_{x+n}=0.40[/math]

(iii) [math]A_{x: n} \frac{1}{}=0.35[/math]

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

Calculate [math]a_{x: n}[/math].

• 9.3
• 9.6
• 9.8
• 10.0
• 10.3

You are given:

(i) Mortality follows the Standard Ultimate Life Table

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

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

Calculate [math]\frac{d}{dt}(\overline{I}\overline{a})_{40:\overline{t}|}[/math] at [math]t=10.5[/math].

• 5.8
• 6.0
• 6.2
• 6.4
• 6.6

(40) wins the SOA lottery and will receive both:

• A deferred life annuity of [math]K[/math] per year, payable continuously, starting at age [math]40+\stackrel{\circ}{e}_{40}[/math] and
• An annuity certain of [math]K[/math] per year, payable continuously, for [math]\stackrel{\circ}{e}_{40}[/math] years

You are given:

(i) [math]\mu=0.02[/math]

(ii) [math]\delta=0.01[/math]

(iii) The actuarial present value of the payments is 10,000

Calculate [math]K[/math].

• 214
• 216
• 218
• 220
• 222

For an annuity-due that pays 100 at the beginning of each year that (45) is alive, you are given:

(i) Mortality for standard lives follows the Standard Ultimate Life Table

(ii) The force of mortality for standard lives age [math]45+t[/math] is represented as [math]\mu_{45+t}^{\text {SULT }}[/math]

(iii) The force of mortality for substandard lives age [math]45+t, \mu_{45+t}^{S}[/math], is defined as:

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

Calculate the actuarial present value of this annuity for a substandard life age 45.

• 1700
• 1710
• 1720
• 1730
• 1740

For a group of 100 lives age [math]x[/math] with independent future lifetimes, you are given:

(i) Each life is to be paid 1 at the beginning of each year, if alive

(ii) [math]\quad A_{x}=0.45[/math]

(iii) [math]{ }^{2} A_{x}=0.22[/math]

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

(v) [math]\quad Y[/math] is the present value random variable of the aggregate payments.

Using the normal approximation to [math]Y[/math], calculate the initial size of the fund needed in order to be [math]95 \%[/math] certain of being able to make the payments for these life annuities.

• 1170
• 1180
• 1190
• 1200
• 1210

You are given:

(i) [math]\quad A_{35}=0.188[/math]

(ii) [math]A_{65}=0.498[/math]

(iii) [math]{ }_{30} p_{35}=0.883[/math]

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

Calculate [math]1000 \ddot{a}_{35: 30}^{(2)}[/math] using the two-term Woolhouse approximation.

• 17,060
• 17,310
• 17,380
• 17,490
• 17,530

For an annual whole life annuity-due of 1 with a 5 -year certain period on (55), you are given:

(i) Mortality follows the Standard Ultimate Life Table

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

Calculate the probability that the sum of the undiscounted payments actually made under this annuity will exceed the expected present value, at issue, of the annuity.

• 0.88
• 0.90
• 0.92
• 0.94
• 0.96