Q1 Calculate 10 4 [27] 1 q + using AM92 mortality. [3]

(Note: You should show your working, but intermediate steps can be shown using

numerical values - no additional notation is required)

Q2 Calculate 2.75 84.5 q using the method of uniform distribution of deaths.

Basis:

Mortality ELT15(Females) [4]

(Note: You should show your working, but intermediate steps can be shown using

numerical values - no additional notation is required)

Q3 The force of interest (t) is a function of time, and at any time t, measured in years is

given by the formula:

0.24 0.02 0 6

( ) 0.12 6

t t

t

t

<

=

<

(i) Find an expression for A(t), the accumulated amount at time of a unit

investment made at time = 0 for 0 < t 6 . [2]

For 6< t , A(t) can be written in the form:

() = +

(ii) Derive the values of and . [4]

(iii) Calculate the present value of $100 due at time t = 7

Q4 A life insurance company issues 25-year decreasing term assurance policies to lives

aged 40 exact. The death benefit, payable at the end of the year of death, is $500,000

in the first policy year, $480,000 in the second policy year thereafter reducing by

$20,000 each year until the benefit is $20,000 in the twenty-fifth and final policy year.

Premiums are payable annually in advance for 25 years or until earlier death.

Show that the annual premium per policy is approximately $643 using the basis

below.

Basis:

Mortality AM92 Ultimate

Rate of Interest 4% per annum

Expenses Ignore