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北美精算师往年真题精选Course8PNovember2001（第二课）

来源：高顿网校 2014-08-20

　　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
　　客观世界只是精神原始的，还没有意识的诗篇。——高顿网校谚语相赠

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