An employer establishes a DC pension plan. Consider a male new entrant aged 30. Suppose that this member will survive to age 65 and retire at that age. The contribution rate is set using the following assumptions.

(i) The employee will use the proceeds at retirement to purchase a pension for his lifetime.

(ii) The target replacement ratio is 60%.

(iii) Contributions are payable yearly in arrear at a fixed percentage of his salary earned during the year.

(iv) Salaries increase at the beginning of each of the following years at a rate 2.25% per year.

(v) Contributions earn investment returns of 8% per year.

(vi) Annuities (life annuity-due) purchased at retirement are priced assuming an interest rate of 5% per year and based on 2001 CSO Mortality Table. It is given that ¨a65 = 11.21147.

(a) Calculate the contribution rate required to meet the target replacement ratio for this member.

(b) Calculate the contribution rate required to meet the target replacement ratio for this member, if the annuity purchased at retirement is a life annuity-due with a 10-year guarantee period. You are given that ¨a75 = 7.99324.