Deck 1: Enrolled Actuary

Question 1

Over a 3-year period, a series of deposits are made to a savings account. All deposits within a given year are equal in size and are made at the beginning of each relevant period. Deposits for each year total $1,200. The following chart shows the frequency of deposits and the interest rate credited for each year: Year Frequency of deposits Interest rate credited during year 1 Semi-annually d (12) = 6.0% 2 Quarterly i (3) = 8.0% 3 Every 2 months ? = 7.0% X = the value of the account at the end of the 3rd year.In what range is X?

A)Less than $3,989
B)$3,989 but less than $4,017
C)$4,017 but less than $4,045
D)$4,045 but less than $4,073
E)$4,073 or more

Answer 1

$4,045 but less than $4,073

Question 2

Terms of two actuarially equivalent annuities: Annuity A Annuity B Issue age 40 40 Type of annuity Perpetuity Life annuity Frequency of payment Monthly MonthlyTiming of payment End of Month End of MonthAmount of each payment P 1,000Selected values: x q x D x Nx 40 0.002125 651 870041 0.002327 607 8049 In what range is P?

A)Less than $860
B)$860 but less than $875
C)$875 but less than $890
D)$890 but less than $905
E)$905 or more

Answer 2

$860 but less than $875

Question 3

A participant will retire at age 80.Selected data:p80 = 0.9521 using unprojected mortalityp81 = 0.9461 using unprojected mortalityi = 6.0%, compounded annuallyX = 20 2 a60 using unprojected mortality Y = 20 2 a60 using post-retirement mortality that is projected with 1% annual mortality improvements from this participant's age 60. Pre-retirement mortality is not projected. In what range is Y/ X ?

A)Less than 1.0140
B)1.0140 but less than 1.0142
C)1.0142 but less than 1.0144
D)1.0144 but less than 1.0146
E)1.0146 or more

Answer 3

1.0142 but less than 1.0144

Question 4

A portfolio consists of a serial bond with the following terms: Face amount $10,000 Coupon rate 5.0% per year, payable annuallyRedemption At par in two equal installments: the first payable in 9 years; the second payable in 10 years.Yield to maturity 4.0% per year, compounded annuallyX = the modified duration of the portfolio.In what range is X?

A)Less than 7.40
B)7.40 but less than 7.60
C)7.60 but less than 7.80
D)7.80 but less than 8.00
E)8.00 or more

Question 5

Retirement benefits for Smith (age 61) and Jones (age 60) payable annually: Smith: a 5-year temporary life annuity-due of XJones: a 10-year certain and life annuity-due of $20,000The present value of Jones's annuity is 4 times that of the present value of Smith's annuity.Selected actuarial factors: a60 = 11.53496a 60:10 = 7.26514a62:4 = 3.58056P61 = 0.99394i = 7.0% per year, compounded annuallyIn what range is X?

A)Less than $13,050
B)$13,050 but less than $13,350
C)$13,350 but less than $13,650
D)$13,650 but less than $13,950
E)$13,950 or more

Question 6

Terms of two actuarially equivalent annuities: Annuity A: $500 at the end of each of the first 3 months, and $1,000 at the end of each of the next 9 months Annuity B: X at the end of each of the first 2 quarters, and 2X at the end of the next 2 quarters Interest rate: 8% per year, compounded monthly In what range is X?

A)Less than $1,770
B)$1,770 but less than $1,800
C)$1,800 but less than $1,830
D)$1,830 but less than $1,860
E)$1,860 or more

Question 7

Selected values from a two-decrement table: q1(1)X = 0.03 q(2)X = 0.10 Each decrement is assumed to be uniformly distributed between ages x and x +1 in the associated single-decrement table. In what range is q(r)X ?

A)Less than 0.1270
B)0.1270 but less than 0.1280
C)0.1280 but less than 0.1290
D)0.1290 but less than 0.1300
E)0.1300 or more

Question 8

Smith pays $950 for an investment that returns $500 at the end of year 3, and $700 at the end of year 4. The price is based on a 2-year spot rate of 5.0% and a 4-year spot rate of 7.0%. X = the year 3 forward rate (i.e., the 2-year deferred, 1-year spot rate).In what range is X?

A)Less than 7.0%
B)7.0% but less than 7.7%
C)7.7% but less than 8.4%
D)8.4% but less than 9.1%
E)9.1% or more

Question 9

Terms of a loan: Amount of loan $75,000 Repayment period 5 years Repayment plans for loan: Repayment Plan #1 Level annual payments at the beginning of each year Repayment Plan #2 Level semi-annual payments at the end of each 6-month period 1000 d(4) = 76.225X = the annual payment under Repayment Plan #1. Y = the total payments in each year under Repayment Plan #2. In what range is X ?Y ?

A)Less than $1,000
B)$1,000 but less than $1,025
C)$1,025 but less than $1,050
D)$1,050 but less than $1,075
E)$1,075 or more

Question 10

Terms of a 20-year annuity-certain: All payments are made on 1/1 Initial payment = $300 Each of the next 9 payments is $300 more than the preceding payment Each of the subsequent 10 payments is $200 less than the preceding payment Interest rate: 7% per year, compounded annually for the first 10 years 6% per year, compounded annually thereafter X = the present value of the annuity immediately before the first payment is made. In what range is X?

A)Less than $18,600
B)$18,600 but less than $18,800
C)$18,800 but less than $19,000
D)$19,000 but less than $19,200
E)$19,200 or more

Question 11

A survival function is defined as follows: sx ( = 1 ? X/250); 0 ? x ? 25l X= 1000 (100 ? x ); x ? 25In what range is 30 /10 q10 ?

A)Less than 0.120
B)0.120 but less than 0.135
C)0.135 but less than 0.150
D)0.150 but less than 0.165
E)0.165 or more

Question 12

In a service table, you are given the following: Number of actives at exact age 40 1,500 Number of voluntary terminations between exact ages 40 and 41 30 Number of involuntary terminations between exact ages 40 and 41 20 Number of disability retirements between exact ages 40 and 41 10 Number of deaths between exact ages 40 and 41 12 All decrements are uniform over the year of age 40 to 41. q = rate of mortality at age 40 in the associated single decrement table.In what range is q?

A)Less than 0.00815
B)0.00815 but less than 0.00817
C)0.00817 but less than 0.00819
D)0.00819 but less than 0.00821
E)0.00821 or more

Question 13

The market value of a fund and its cash flows at various dates in a calendar year are shown below: Date Value of fund before withdrawals Withdrawals1/1 $300,000 $0 m months after 1/1 315,000 15,000 2m months before 12/31 315,000 15,000 12/31 315,000 0The dollar-weighted rate of return for the year is 16.0%. In what range is m?

A)Less than 2.1
B)2.1 but less than 2.5
C)2.5 but less than 2.9
D)2.9 but less than 3.3
E)3.3 or more

Question 14

Smith has the option of receiving a benefit in the form of an annuity beginning in one year.The annuities, each of which is actuarially equivalent, are:Option 1 A life annuity of $1,000 per yearOption 2 A life annuity of X per year, decreasing to 50% of X payable to Smith's spouse after Smith's death Option 3 A life annuity of $875 per year, payable while either Smith or Smith's spouse is aliveIn what range is X?

A)Less than $920
B)$920 but less than $925
C)$925 but less than $930
D)$930 but less than $935
E)$935 or more

Question 15

Data for participant Smith: Age 65Years of service 10 Average compensation for highestconsecutive 3 years of participation $50,000 The plan provides the qualified joint and 100% survivor annuity on a fully subsidized basis. Consider the following statement:The maximum annual annuity Smith can receive in the form of a qualified joint and 100% survivor annuity is $50,000.Is the above statement true or false?

Question 16

A plan sponsor borrows $100,000 from the plan. The loan, plus a reasonable rate of interest, is repaid within 90 days. Consider the following statement: The loan is a prohibited transaction.Is the above statement true or false?

Question 17

A sponsor maintains Plan A and Plan B. Information for the 2012 plan year: FTAP Unfunded vested benefitsPlan A 75% $13,000,000 Plan B 84% $50,000,000 Consider the following statement: Reporting under ERISA section 4010 is required for this sponsor for the 2012 plan year.Is the above statement true or false?

Question 18

Funding balances at 1/1/2012: $0 Normal retirement benefit: $20 per year of service On 2/1/2012, the 2012 AFTAP is certified at 75% On 3/1/2012, the plan's benefit formula is amended to: $20 per month per year of service accrued through 2/29/2012, plus $25 per month per year of service accrued after 3/1/2012. No contributions are made during 2012. Consider the following statement: The amendment can take effect on 3/1/2012.Is the above statement true or false?

Question 19

Consider the following statement: The only circumstance that would allow for any portion of plan assets to be returned to a plan sponsor is a plan termination.Is the above statement true or false?

Question 20

Plan effective date: 1/1/2001 The plan uses the most restrictive vesting requirements and the 7-year graded vesting schedule. An employee works over 1,000 hours in each year of employment.Employee data:Date of birth 1/1/1985 Date of hire 1/1/2002 Date of termination 12/31/2005 Date of rehire 1/1/2009 Consider the following statement: The employee is 100% vested as of 1/1/2012.Is the above statement true or false?

Question 21

Consider the following statement: Upon the plan administrator's request, an enrolled actuary must provide supplemental advice or explanation relative to an actuarial report certified by the enrolled actuary.Is the above statement true or false?

Question 22

A plan provides a pre-retirement death benefit equal to the minimum qualified pre-retirement survivor annuity under IRC section 417 plus a $10,000 immediate lump sum. These benefits are provided at no charge to the participants. Consider the following statement with regard to the PBGC Premium Funding Target: The full value of the pre-retirement death benefit is included in the Premium Funding Target for each participant who has completed the plan's vesting requirements on the Unfunded Vested Benefit valuation date. Is the above statement true or false?

Question 23

Plan effective date: 1/1/1990 Consider the following statement: The plan administrator must provide each participant with a copy of the summary plan description no later than 90 days after an employee becomes a participant in the plan. Is the above statement true or false?

Question 24

Normal retirement age: 62Plan assumptions: Interest 4.0% Mortality 1994 GARDeath benefit prior to retirement is the present value of accrued benefits. Benefit at late retirement is the greater of continued accruals and an actuarial increase. Selected data for Smith: Date of birth 12/31/1942 Date of hire 1/1/2000 Date of participation 1/1/2006 Date of retirement 12/31/2012 Compensation for each year of service $225,000Selected commutation functions:5% and applicable mortalityx N(12)x D x N(12)X Dx62 598,284 46,091 1,466,321 82,76965 470,592 38,961 1,232,637 72,90070 301,642 28,773 904,410 58,535In what range is Smith's annual IRC section 415 limit as of 12/31/2012?

A)Less than $175,000
B)$175,000 but less than $190,000
C)$190,000 but less than $205,000
D)$205,000 but less than $220,000
E)$220,000 or more

Question 25

Employer A is a contributing employer to a multiemployer plan. Method for calculating withdrawal liability: Rolling-5 with mandatory de minimis rule.Employer A completely withdraws from the plan on 12/31/2011. Total Total 12/31 Total contributions Total unfunded contributions withdrawn contributions vested benefits OutstandingYear all employers employers Employer A (all employers) claims*2005 $19,600,000 $500,000 $760,000 $0 $0 2006 23,400,000 450,000 650,000 0 0 2007 25,300,000 350,000 870,000 0 0 2008 28,900,000 625,000 905,000 60,200,000 0 2009 29,100,000 800,000 805,000 70,900,000 1,200,000 2010 25,200,000 1,225,000 725,000 75,200,000 2,500,000 2011 27,800,000 1,500,000 225,000 78,000,000 2,750,000 * For withdrawal liability that can reasonably be expected to be collected with respect to employers who withdrew before the end of the plan year. In what range is the withdrawal liability for Employer A?

A)Less than $2,100,000
B)$2,100,000 but less than $2,150,000
C)$2,150,000 but less than $2,200,000
D)$2,200,000 but less than $2,250,000
E)$2,250,000 or more

Question 26

Data for a plan in 2012: Location A B C D Number of employees 41 19 15 XThe plan covers all employees of locations B and D only. Location C is collectively bargained.No employees terminated during 2012 and none are statutorily excludable from the plan. The plan covers at least one HCE. What is the minimum number of employees that must be in Location D so that the plan will pass the participation requirement of IRC section 401(a)(26)?

A)Less than 9
B)9 but less than 14
C)14 but less than 19
D)19 but less than 24
E)24 or more

Question 27

A defined benefit plan terminates with excess assets and is amended within the 60 day period prior to the plan termination date to provide a 5% pro-rata increase of participant benefits as of the termination date. The plan sponsor establishes a defined contribution plan as a qualified replacement plan and transfers into this plan the minimum amount necessary to lower the excise tax rate on any reversion to less than 50%. Selected data as of the asset distribution date: Market value of assets $2,100,000 Termination liability prior to 5% pro-rata increase $1,600,000X= the amount of the actual excise tax due from the employer. Y = the amount of the excise tax that would have been due had the qualified replacement plan not been established. In what range is X - Y ?

A)Less than $132,000
B)$132,000 but less than $150,000
C)$150,000 but less than $168,000
D)$168,000 but less than $186,000
E)$186,000 or more

Question 28

Type of plan: Statutory hybrid planAccount balance: The sum of pay credits and interest creditsPay credits: 3% of annual pay, credited at the end of the yearInterest credits: Equal to the actual annual rate of return on plan assets multiplied by the beginning of year account balance Vesting: The minimum vesting schedule allowedData for participant Smith: Date of hire 1/1/2008 Date of termination 12/31/2011 Compensation (each year) $50,000 Historical returns on plan assets: 2008 8% 2009 6% 2010 2% 2011 ?22% The plan provides for a lump sum in the amount of the vested account balance.In what range is Smith's lump sum payable at 1/1/2012?

A)Less than $3,650
B)$3,650 but less than $4,450
C)$4,450 but less than $5,250
D)$5,250 but less than $6,050
E)$6,050 or more

Question 29

An employer sponsors two plans: Plan A for Division A and Plan B for Division BPlan A eligibility: 12 months of service Plan B eligibility: 6 months of service All employees are eligible to participate on the 1/1 or 7/1 coincident with or following the completion of eligibility requirements. Plans A and B require 1,000 hours of service to benefit in the plan (however, eligibility is determined on an elapsed time basis). Otherwise excludable employees are not tested separately.No employee is in more than one plan and none are collectively bargained. The plan sponsor does not aggregate Plans A and B for purposes of the coverage requirement of IRC section 410(b). Data for all employees during 2011:Number of Date of Hours End ofemployees hire worked Division year status 20 1/1/2010 2,000 A active HCE40 1/1/2010 2,000 A active NHCE 5 1/1/2010 250 A terminated NHCE10 1/1/2010 2,000 B active HCE25 1/1/2010 2,000 B active NHCE15 9/1/2010 2,000 B active NHCE10 1/1/2010 250 B terminated NHCEIn what range is the ratio percentage for Plan A for the 2011 plan year?

A)Less than 72.00%
B)72.00% but less than 79.00%
C)79.00% but less than 86.00%
D)86.00% but less than 93.00%
E)93.00% or more

Question 30

Type of plan: MultiemployerMethod for determining withdrawal liability: Rolling-5 with maximum permissible deductible under the optional de minimis ruleEmployer A completely withdraws from the plan on 12/31/2011. No other employers have ever withdrawn from the plan. Total 12/31Total base Total Total unfundedunits all contributions Total base units contributions vested benefitsYear employers all employers Employer A Employer A (all employers)2004 2,025,000 $13,162,000 37,000 $240,000 $0 2005 2,150,000 13,975,000 41,000 266,000 0 2006 2,300,000 16,100,000 45,000 315,000 0 2007 2,225,000 16,687,000 48,000 360,000 12,850,000 2008 2,150,000 17,200,000 47,000 376,000 16,200,000 2009 2,300,000 19,550,000 45,000 382,000 24,500,000 2010 2,350,000 21,150,000 41,000 369,000 10,750,000 2011 2,425,000 21,825,000 34,000 306,000 9,650,000 In what range is the withdrawal liability for Employer A?

A)Less than $137,500
B)$137,500 but less than $157,500
C)$157,500 but less than $177,500
D)$177,500 but less than $197,500
E)$197,500 or more

Question 31

A plan pays mandatory lump sums less than or equal to $1,000. Elective lump sums are allowed in any amount in excess of $1,000. The plan terminated in a standard termination. Data for missing participant Smith, not in pay status, as of deemed distribution date: Lump sum based on plan provisions $5,600 Present value based on PBGC lump sum assumptions 5,900 Present value based on PBGC missing participant annuity assumptions 5,500 Values do not include any expense loads.In what range is the Designated Benefit for Smith?

A)Less than $5,610
B)$5,610 but less than $5,720
C)$5,720 but less than $5,830
D)$5,830 but less than $5,940
E)$5,940 or more

Question 32

Data for the only nine participants that have ever been in the plan: Stock Present value of DistributionsParticipant ownership 2012 accrued benefit asnumber percentage compensation 2011 2012 of 12/31/20121 50.0 $200,000 $0 $50,000 $200,0002 0.5 200,000 0 0 30,0003 3.0 160,000 0 0 80,0004 3.0 125,000 0 0 50,0005 6.0 100,000 0 0 60,0006 0 70,000 40,000 20,000 20,0007 0 50,000 0 40,000 40,0008 0 30,000 0 0 30,0009 0 0 0 0 100,000 Participant 9 terminated employment on 11/1/2011. All others were employed for the entire 2011 and 2012 plan years. Participants 1 and 5 are the only officers. The stock ownership percentages and officer statuses have never changed since the company's inception. Present values of accrued benefits as of 12/31/2012 do not include the value of any distributions received. No distributions were ever paid from the plan prior to 2011.In what range is top-heavy ratio for 2013?

A)Less than 0.51
B)0.51 but less than 0.56
C)0.56 but less than 0.61
D)0.61 but less than 0.66
E)0.66 or more

Question 33

A plan provides a preretirement death benefit equal to the present value of the accrued benefit. Plan's actuarial equivalence assumptions: Interest rate 7.5% Pre-commencement mortality table None Post-commencement mortality table Applicable mortality under IRC section 417(e) Early retirement benefit is based on plan actuarial equivalence. Selected data for participant Smith: Date of birth 12/31/1952 Date of hire 1/1/2005 Date of participation 1/1/2006 Date of retirement 12/31/2012 Compensation for each year $150,000 Form of benefit elected Life annuitySingle life annuity factors based on the applicable mortality table at selected retirement ages and interest rates: Age 5.0% 7.5%60 13.56 10.84 62 12.98 10.50In what range is Smith's IRC section 415 limit as of 12/31/2012?

A)Less than $118,000
B)$118,000 but less than $121,000
C)$121,000 but less than $124,000
D)$124,000 but less than $127,000
E)$127,000 or more

Question 34

Information as of 1/1/2012: Standard Premium Funding Target $100,000,000Actuarial (market) value of assets before reflecting contributions receivable 76,000,000Funding standard carryover balance 2,000,000Prefunding balance 0Contributions paid during 2012:Date paid Amount For plan year3/31/2012 $800,000 20114/15/2012 1,000,000 20127/15/2012 1,000,000 20129/15/2012 4,500,000 201110/15/2012 1,000,000 2012Effective interest rates:Plan year 2011 6.25% Plan year 2012 5.50% The plan administrator has not made an election to use the Alternative Premium Funding Target.In what range is the PBGC Variable-rate premium for 2012?

A)Less than $150,000
B)$150,000 but less than $160,000
C)$160,000 but less than $170,000
D)$170,000 but less than $180,000
E)$180,000 or more

Question 35

Consider the following plans that are sponsored by four unrelated companies: Non-excludable employees Benefiting employees HCE NHCE NCE NHCEPlan I 5 100 1 40 Plan II 10 50 10 0 Plan III 5 95 5 35 Plan IV 50 100 0 40 How many of these plans satisfy the participation requirement of IRC section 401(a)(26)?

A)0
B)1
C)2
D)3
E)4

Question 36

Eligibility: 1 year of service (elapsed time) Entry dates: 1/1 and 7/1 Excluded employees: Hourly employees and non-resident aliensHours needed for accrual: 1,000 Employee Category Date of hire Date of termination Hours in 20121 Salaried 4/1/2010 1,000 2 Hourly 4/1/2010 1,0003 Non-resident alien 4/1/2010 1,0004 Salaried 4/1/2011 1,000 5 Salaried 9/1/2011 1,0006 Salaried 4/1/2010 6/30/2012 1,000 7 Salaried 4/1/2010 6/30/2012 4008 Hourly 4/1/2010 6/30/2012 1,0009 Hourly 4/1/2010 6/30/2012 400The simplified testing method is not used. How many employees may be treated as excludable for purposes of IRC section 401(a)(26) for 2012?

A)Fewer than 3
B)3
C)4
D)5
E)6 or more