You are given:

(i) [math]\quad q_{60}=0.01[/math]

(ii) Using [math]i=0.05, A_{60: \overline{3 |}}=0.86545[/math]

Using [math]i=0.045[/math] calculate [math]A_{60: \overline{3 |}}[/math].

• 0.866
• 0.870
• 0.874
• 0.878
• 0.882

For a 2 -year deferred, 2 -year term insurance of 2000 on [65], you are given:

(i) The following select and ultimate mortality table with a 3-year select period:

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

(iii) The death benefit is payable at the end of the year of death

Calculate the actuarial present value of this insurance.

• 260
• 290
• 350
• 370
• 410

You are given the following extract of ultimate mortality rates from a two-year select and ultimate mortality table:

The select mortality rates satisfy the following:

• [math]q_{[x]}=0.7 q_{x}[/math]
• [math]q_{[x]+1}=0.8 q_{x+1}[/math]

You are also given that [math]i=0.04[/math].

Calculate [math]A_{[50]: \overline{3 |}}^{1}[/math].

• 0.08
• 0.09
• 0.10
• 0.11
• 0.12

You are given:

(i) [math]\quad q_{60}p_{60}=0.02[/math]

(ii) Using [math]i=0.04, A_{60: \overline{3 |}}=0.86545[/math]

Using [math]i=0.03[/math] calculate [math]A_{60: \overline{3 |}}[/math].

• 0.865
• 0.869
• 0.870
• 0.8712
• 0.8725

For a 15-year Pure Endowment of [math]1[/math] on a life aged [math](x)[/math], you are given:

The Coefficient of Variation of the present value random variable [math]Z[/math] is [math]1.25[/math].

Calculate the probability that the endowment benefit is paid out, [math]{}_{15} p_{x}[/math].

• 0.39
• 0.41
• 0.43
• 0.45
• 0.47

You are given the following information:

(i) The Expected Present Value (EPV) of an [math]n[/math]-year temporary life annuity-due on [math](x)[/math] is: [math]\ddot{a}_{x:\overline{n}|} = \mathbf{12.00}[/math] (denoted as [math]a_{x:\overline{n}|}[/math] for brevity).

(ii) The EPV of the whole life annuity-due on [math](x)[/math] is: [math]\ddot{a}_x = \mathbf{15.00}[/math].

(iii) The EPV of the whole life annuity-due on [math](x+n)[/math] is: [math]\ddot{a}_{x+n} = \mathbf{13.00}[/math].

(iv) The annual effective interest rate is [math]\mathbf{i = 5\%}[/math].

Calculate the Expected Present Value of the [math]n[/math]-year pure endowment (i.e., [math]v^n \cdot {}_n p_x[/math]).

• 0.200
• 0.231
• 0.250
• 0.867
• 3.000

For a special increasing whole life insurance on (40), payable at the moment of death, you are given:

(i) The death benefit at time [math]t[/math] is [math]b_{t}=1+0.2 t, \quad t \geq 0[/math]

(ii) The interest discount factor at time [math]t[/math] is [math]v(t)=(1+0.2 t)^{-2}, \quad t \geq 0[/math]

(iii) [math]\quad{ }_{t} p_{40} \mu_{40+t}= \begin{cases}0.025, & 0 \leq t\lt40 \\ 0, & \text { otherwise }\end{cases}[/math]

(iv) [math]Z[/math] is the present value random variable for this insurance

Calculate [math]\operatorname{Var}(Z)[/math].

• 0.036
• 0.038
• 0.040
• 0.042
• 0.044

For a 30 -year term life insurance of 100,000 on (45), you are given:

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

(ii) Mortality follows the Standard Ultimate Life Table

(iii) [math]\delta=0.05[/math]

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

Calculate the [math]95^{\text {th }}[/math] percentile of the present value of benefits random variable for this insurance.

• 30,200
• 31,200
• 35,200
• 36,200
• 37,200

For a 3-year term insurance of 1000 on (70), you are given:

(i) [math]\quad q_{70+k}^{\text {SULT }}[/math] is the mortality rate from the Standard Ultimate Life Table, for [math]k=0,1,2[/math]

(ii) [math]\quad q_{70+k}[/math] is the mortality rate used to price this insurance, for [math]k=0,1,2[/math]

(iii) [math]\quad q_{70+k}=(0.95)^{k} q_{70+k}^{S U L T}[/math], for [math]k=0,1,2[/math]

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

Calculate the single net premium.

• 29.05
• 29.85
• 30.65
• 31.45
• 32.25

For a 25 -year pure endowment of 1 on [math](x)[/math], you are given:

(i) [math]\quad Z[/math] is the present value random variable at issue of the benefit payment

(ii) [math]\operatorname{Var}(Z)=0.10 E[Z][/math]

(iii) [math]{ }_{25} p_{x}=0.57[/math]

Calculate the annual effective interest rate.

• 5.8%
• 6.0%
• 6.2%
• 6.4%
• 6.6%