# FINA3220A Assignment 1

```FINA3220A Life Contingencies I
Second Term 2018-2019
Assignment 1
Hand in the solutions on or before 31 January 2019.
1.
The following function has been proposed as the survival function S0  x  for a mortality
model:
18000  110 x  x 2
G  x 
.
18000
(a) What is the implied limiting age ?
(b) Verify that the function G satisfies the criteria for a survival function.
(c) Calculate 20 p0 .
(d) Determine the survival function for a life aged 20.
(e) Calculate the probability that a life aged 20 will die between ages 30 and 40.
(f) Calculate the force of mortality at age 50.
2.
You are given the survival function
9000  10 x  x 2
S0  x  
,
9000
Calculate the exact value of q50  50 .
0  x  90.
3.
If the force of mortality is constant and equal to ln(10/9) from age 76 to age 80, how many of
1000 persons aged 76 will be expected to survive to age 80?
4.
Calculate
5.
You are given:
20
p40 , given that (x) = kx for all x > 0, and

S0  t  

e 40  2 e80

10
p35  0.81 .
k2 t
, 0  t  k 2 , k  0.
k


Calculate e60 .
6.
You are given:



Hens lay an average of 30 eggs each month until death.
m
The survival function for hens is S0  m   1  , 0  m  72, where m is in months.
72
100 hens have survived to age 12 months.
Calculate the expected total number of eggs to be laid by these 100 hens in their remaining
7.
You are given the survival function S0  x  
1
. Determine the median future lifetime of (y).
1 x
1
8.
Suppose that Gompertz’ law applies with 30  0.000130 and  40  0.000344. Calculate
9.
Suppose that De Movire’s law applies with 60  0.02. Show that the future lifetime random
10
p40 .

variable for (x) has a uniform distribution and e 40  35.
10. Suppose that Makeham’s law of mortality is adopted with parameters A = 0.0004, B = 0.0004
and c = 1.08.
(a) Construct a table of px for integer x from age 0 to age 130, using EXCEL.
(b) Use the table to determine the age last birthday at which a life currently aged 50 is most
likely to die.
(c) Use the table to calculate e70 .

(d) Using a numerical approach, calculate e70 .
For Question 10, submit your EXCEL files through Blackboard.
2
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