高顿网校小编提示：以下是北美精算师往年真题精选Course8PNovember2001（第二课），往年真题，不可轻视。
　　3. (8 points) You are the actuary for a company that sponsors a non-contributory defined
　　benefit pension plan.
　　You are given:
　　Plan Provisions
　　Retirement benefit: $20 per month, per year of service
　　Normal form of pension: Life only, payable monthly in advance
　　Normal retirement age: 60
　　Early retirement reduction: 5% per year that retirement precedes age 60
　　Other ancillary benefits: None
　　Actuarial Assumptions and Method
　　Interest rate: 7.0% per annum
　　Retirement rates: 10% per annum, at the beginning of each year,
　　from age 57 through 59; 100% at age 60
　　Pre-retirement decrements: None
　　Actuarial cost method: Unit Credit
　　&& a57
　　b12g = 10.0
　　&& a58
　　b12g = 9.0
　　&& a59
　　b12g = 8.0
　　&& a60
　　b12g = 7.0
　　Financial Information
　　Assets at January 1, 2001: $100,000
　　2001 employer contribution: None
　　Fund rate of return in 2001: 2%
　　Participant Data as at January 1, 2001
　　Member Age Service
　　Jean 57 25
　　Kelly 58 29
　　COURSE 8: November 2001 - 7 - GO TO NEXT PAGE
　　Retirement Benefits,
　　Pension Funding Mathematics Segment
 
　　3. (CONTINUED)
　　(a) Calculate the unfunded accrued liability and normal cost as at January 1, 2001.
　　(b) On December 31, 2001, Kelly retires. On December 31, 2001, Pat transfers into
　　the plan at age 45 and $10,000 is transferred to recognize 10 years of Pat’s prior
　　service.
　　Calculate the unfunded accrued liability as at January 1, 2002.
　　(c) Calculate the gains and losses by source for 2001.
　　Show all work.
　　COURSE 8: November 2001 - 8 - GO TO NEXT PAGE
　　Retirement Benefits,
　　Pension Funding Mathematics Segment
 
　　4. (4 points) You are the actuary for a company that sponsors a defined benefit pension
　　plan.
　　You are given:
　　Plan Provisions
　　Retirement benefit: $30 per month, per year of service
　　Normal form of payment: Five years certain and life thereafter, payable
　　monthly in advance
　　Optional form of payment: Actuarially equivalent 75% joint and
　　survivor annuity
　　Normal retirement age: 65
　　Early retirement reduction: Actuarial equivalence
　　Other ancillary benefits: None
　　Actuarial equivalence: Based on valuation assumptions
　　Actuarial Assumptions and Method
　　Interest rate: 7.0% per annum
　　Retirement age: 65
　　Pre-retirement decrements: None
　　Actuarial cost method: Entry Age Normal
　　Member Spouse Member: Spouse
　　&& a60
　　b12g = 10.8387 && a57
　　b12g = 12.5296 && a60:57
　　b12g = 9.7460
　　&& a65
　　b12g = 9.7004 && a62
　　b12g = 11.6834 && a65:62
　　b12g = 8.5126
　　&& a70
　　b12g = 8.4642 && a67
　　b12g = 10.6379 && a70:67
　　b12g = 7.1863
　　5 p60 = 0.9446
　　5 p65 = 0.9039
　　The following member retires on January 1, 2001:
　　Data as at January 1, 2001
　　Member’s age: 60
　　Spouse’s age: 57
　　Years of service: 35
　　COURSE 8: November 2001 - 9 - GO TO NEXT PAGE
　　Retirement Benefits,
　　Pension Funding Mathematics Segment
 
　　4. (CONTINUED)
　　(a) Calculate the experience gain or loss on January 1, 2001 caused by the retirement
　　of the member.
　　(b) Calculate the member’s pension under the optional form of payment.
　　Show all work.
　　COURSE 8: November 2001 - 10 - STOP
　　Retirement Benefits,
　　Pension Funding Mathematics Segment
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