You are given

for [math]0 \lt t \lt 100[/math].

Calculate [math]\stackrel{\circ}{e}_{75:\overline{10|}}[/math].

• 6.6
• 7.0
• 7.4
• 7.8
• 8.2

You are given:

i) [math]\mu_{x+t}=\beta t^{2}, t \geq 0[/math]

ii) [math]l_{x}=1000[/math]

iii) [math]l_{x+10}=400[/math]

Calculate [math]1000 \beta[/math].

• 2.75
• 2.80
• 2.85
• 2.90
• 2.95

For the country of Bienna, you are given:

(i) Bienna publishes mortality rates in biennial form, that is, mortality rates are of the form:

(ii) Deaths are assumed to be uniformly distributed between ages [math]2 x[/math] and [math]2 x+2[/math], for [math]x=0,1,2, \ldots[/math]

(iii) [math]{ }_{2} q_{50}=0.02[/math]

(iv) [math]{ }_{2} q_{52}=0.04[/math]

Calculate the probability that (50) dies during the next 2.5 years.

• 0.02
• 0.03
• 0.04
• 0.05
• 0.06

You are given the survival function [math]S(x)[/math] which is defined as:

And [math]S(x) = 0[/math] for [math]x \gt 50[/math].

Calculate the complete expected temporary life expectancy [math]\stackrel{\circ}{e}_{10:\overline{20|}}[/math] for an individual currently aged 10, measured over a future term of 20 years.

• 6.27
• 8.62
• 11.66
• 13.72
• 18.23

A life insurance calculation requires a constant force of mortality, [math]\mu[/math], to be applied over a continuous two-year interval.

You are given that the probability of a person dying between time [math]t=0.2[/math] and time [math]t=1.4[/math] (a duration of 1.2 years) is stipulated to be:

Determine the constant rate of mortality [math]\mu[/math]

• 0.0831
• 0.1267
• 0.138
• 0.407
• 0.81

For the country of Triennia, you are given:

(i) Triennia publishes mortality rates in triennial form, that is, mortality rates are of the form:

(ii) Deaths are assumed to be uniformly distributed between ages [math]3 x[/math] and [math]3 x+3[/math], for [math]x=0,1,2, \ldots[/math]

(iii) [math]{ }_{3} q_{48}=0.03[/math]

(iv) [math]{ }_{3} q_{51}=0.06[/math]

Calculate the probability that (48) dies during the next 4 years.

• 0.03
• 0.04
• 0.0494
• 0.06
• 0.09

The SULT Club has 4000 members all age 25 with independent future lifetimes. The mortality for each member follows the Standard Ultimate Life Table.

Calculate the largest integer [math]N[/math], using the normal approximation, such that the probability that there are at least [math]N[/math] survivors at age 95 is at least [math]90 \%[/math].

• 800
• 815
• 830
• 845
• 860

You are given the following extract from a table with a 3-year select period:

[math]e_{64}=5.10[/math]

Calculate [math]e_{[61]}[/math].

• 5.30
• 5.39
• 5.68
• 5.85
• 6.00

For a mortality table with a select period of two years, you are given:

The force of mortality is constant between integral ages.

Calculate [math]1000_{2.5} q_{[50]+0.4}[/math].

• 15.2
• 16.4
• 17.7
• 19.0
• 20.2

A club is established with 2000 members, 1000 of exact age 35 and 1000 of exact age 45 . You are given:

(i) Mortality follows the Standard Ultimate Life Table

(ii) Future lifetimes are independent

(iii) [math] N[/math] is the random variable for the number of members still alive 40 years after the club is established

Using the normal approximation, without the continuity correction, calculate the smallest [math]n[/math] such that [math]\operatorname{Pr}(N \geq n) \leq 0.05[/math].

• 1500
• 1505
• 1510
• 1515
• 1520