Microeconomics questions

(i) Express tVx in terms of Ax and Ax+t. Hence, or otherwise, find the values of nVx and

nVx+n, given that

1 ? Ax+2n = Ax+2n ? Ax+n = Ax+n ? Ax

(ii) Calculate 1V40 given that P40 = .01536, p40 = .99647 and i = .05.

Consider an n-year pure endowment policy, issued to (x), with sum assured 1 and with annual

premiums payable throughout the duration of the policy. In the event of death within the n

years, all premiums paid will be returned without interest at the end of the year of death.

Obtain expressions for the reserve at duration t

(i) prospectively and

(ii) retrospectively.

Using commutation functions, show that your expressions are equal. (Assume that the premium

due at time t has not yet been paid.)

(Difficult)

Given that Px = 0.02, nVx = 0.06, and P1x:n = 0.25, find P

1=x:n .

Ten years ago a life office issued a 20-year endowment assurance without profits to (35). The

sum assured is 10000, payable at the end of the year of death (or on survival for 20 years),

and premiums are payable annually in advance. Using A1967-70 ultimate 6%, and ignoring

expenses, calculate

(i) the annual premium;

(ii) the reserve, assuming that the premium now due has been paid.

(Difficult) You are given:

(i) Px = 0.01212

(ii) 20Px = 0.01508

(iii) P1x:10 = 0.06942

(iv) 10Vx = 0.11430

Calculate 2010Vx .

A whole life assurance with sum assured 100,000 payable at the end of the year of death was

purchased by a life aged 30. The policy has annual premiums payable throughout life.

The basis for calculating reserves for this policy is as follows:

net premium method: A1967-70 ultimate, 5% p.a. interest.

Estimate the policy value at duration 28 1

4

by interpolation.

Describe the following terms briefly:

(i) net premium reserves;

(ii) Zillmerised reserves;

1,000 male and 1,000 female subjects were chosen at random by a researcher and cross-classified according to sex and to whether or not they were colour-blind, giving the following table: male female normal 908 993 colour-blind 92 7 (i) Perform a y" test on this contingency table to show that there is overwhelming evidence against the hypothesis that there is no association between an individual's sex and whether or not the individual is colour-blind. [5 (ii) A genetic model states that the human population is split in the proportions illustrated in the following table, where q (0