Answer the questions below well

.13 It is desired to set up a pension scheme for the group of employees described below. For each member there is recorded his exact age, his exact length of service with the company, and his annual rate of salary. Seivice Salary (Years) The scheme will provide pensions of El th of \"pensionable salary\" for each year of service {fractions of a year being included] and on death or withdrawal from service a return will be made of the member's contributions with 3% compound interest. All members will contribute at the same rate and the employer will contribute the same amount as each member. The contribution rate will be such as to provide exactly the benets for future service. The basie of \"Formulae and Tables\" is to be used. {a} Assuming that pensionable salary is the average annual earnings over the threeyear period ending on the retirement date, calculate the contribution rate payable by each member. {b} Calculate also the total liability for past service benets. The employer wishes to meet this liability by paying additional contributions proportional to future salary payments. At what rate should these additional contributions be made? {c} Immediately after the scheme is set up as described above the 45 year old member with 5 years of service withdraws. Is the position of the fund improved or worsened by this with drawal? .T The pension scheme of a large company provides the following benets, among others: {1} on death in service of married members: a spouse's pension of onethird of the member's annual salary at the date of death, {2} on death after normal retirement of the member at age or after illhealth retirement at an earlier age: a spouse's pension of 1% of annual salary at the date of retirement for each year of scheme membership {including fractions of a year}, no pension is payable if the marriage has taken place after the member's retirement date. Assume that a service table has been constructed, and that the proportion of members mar ried at exact y is by. Assume further that spouses are the same age as members, and that a unisex mortality table is used for all calculations, with the age rated up by 5 years on illhealth retirement. You are given the age nearest birthday, current salary rate and years of past service {including fractions} of each member. Spouse's pension is payable monthly in advance, begim1ing immediately on the death of the member. {i} Using the rate of interest 1' per annum, nd formulae for the mean present value of each of the benets {1] and {2} above for a member aged 1' {I