Calculate:

A certain friendly society recruits only married men aged under 55. The society provides the

following benefits:

(i) immediately on the death of the member at any age, 2,000,

(ii) during the first 10 years of membership, immediately on the death of the member's wife

before her husband, 500,

(iii) on survival of the member to age 65, an annuity of 10 per week for life, and

(iv) during any spell of sickness of the member before age 65, 10 per week reducing to 6

per week after 3 months' sickness.

The basis for all calculations is:

mortality of members: E.L.T. No.12 - Males

mortality of wives: E.L.T. No. 12 - Males with an age-deduction of 5 years

interest: 4% per annum

sickness: Manchester Unity 1893-97 AHJ

expenses: 5% of all contributions, including those waived during sickness

Wives of members are taken as being of the same age as their husbands; there is no benefit

on the death of wives of marriages taking place after entry to the society, and the possibility

of divorce is to be ignored. There is no waiting period and the off-period is as in the Tables

provided. The possibility of withdrawal is ignored.

(a) Calculate the weekly contribution rate, waived during sickness and ceasing at age 65 or

the previous death of the member, for an entrant aged 25.

(b) Calculate the reserve for a member aged 35 who joined at age 25.

Note Use Simpson's rule for approximate integration, i.e.

Z b

a

f(t) dt '

b ? a

6

[f(a) + 4f(

a + b

2

) + f(b) Friendly Society issues policies providing the following benefits:

(i) A sickness benefit of 25 per week for the first 13 weeks of sickness and 12.50 per week

thereafter, benefit ceasing at age 60. Contributions are waived during sickness.

(ii) On death before age 60, a lump sum of 1,000 plus a return of contributions (including

any waived) without interest.

(iii) On survival to age 60, a lump sum of 2,000.

Contributions are payable by level weekly amounts until age 60. There is a six-month waiting

period for the sickness benefit (including the premium waiver) and the off-period may be

assumed to be the same as that underlying the tables in "Formulae and Tables for Actuarial

Examinations".

(a) Calculate the weekly contribution payable by a new member aged 35 on the basis given

below.

(b) Calculate the reserve (on the basis given below) to be held for this member five years after

he joins the Society.

Basis: English Life Table No. 12 - Males

Manchester Unity Sickness Experience 1893-97, Occupation Group AHJ

interest 4% per annum.

expenses are 5% of all premiums (including those waived).

Using the assumption of a uniform distribution of deaths in each year of age and the Illustrative Life Table with interest at the effective annual rate of 6%, Calculate a. am, a5\b. If Y = Jan OST <>