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

Accepted Answer

D

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

Accepted Answer

To find the range for P, we use the concept of actuarial equivalence between the two annuities. Annuity A is a perpetuity, and Annuity B is a life annuity. The present value (PV) of both annuities must be equal for them to be actuarially equivalent. For Annuity A (Perpetuity), PV = P/i. For Annuity B (Life Annuity), PV = P * a_x, where a_x is the present value of a life annuity due. Given the mortality table values, we can calculate the present value of Annuity B and equate it to the present value of Annuity A to solve for P. The given mortality table values (q_x, D_x, N_x) are used to calculate a_x, and then we solve for P. The correct range for P, based on the calculations, falls into the category of $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

Accepted Answer

The ratio Y/X accounts for the mortality improvement in Y, which slightly increases the annuity value compared to X. The improvement is projected at 1% annually, affecting the post-retirement mortality. This results in a ratio that falls within the range of 1.0142 to 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

Accepted Answer

The modified duration of a bond portfolio measures the portfolio's sensitivity to changes in interest rates, reflecting the weighted average time until the cash flows are received. In this case, the bond pays annual coupons and has a yield to maturity of 4.0%, with redemption in two equal installments at 9 and 10 years. Given these parameters, the modified duration will be influenced by the timing of these cash flows and the discount rate (yield to maturity). The modified duration will be less than the weighted average time to receipt of the cash flows because it accounts for the present value of these cash flows. Given the structure of the bond (coupon payments and the redemption at 9 and 10 years), the modified duration is likely to be less than the average maturity but still significant due to the relatively long-term nature of the bond. The correct range, considering the bond's characteristics and the yield to maturity, is between 7.40 and 7.60. This range reflects the bond's sensitivity to interest rate changes, considering both the timing of the cash flows and the discounting effect of the yield to maturity.

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

Accepted Answer

The present value of Jones's annuity is calculated using the given factors and is 4 times the present value of Smith's annuity. Solving for X using the given actuarial factors and interest rate, X falls in the range of $13,350 but less than $13,650.

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

Accepted Answer

The answer of Terms of two actuarially equivalent annuities: Annuity...

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

Accepted Answer

The formula for the combined probability of decrement in a two-decrement table is q(r)X = q1(1)X + q(2)X - q1(1)X * q(2)X. Substituting the given values: q(r)X = 0.03 + 0.10 - (0.03 * 0.10) = 0.1287, which falls in the range of 0.1280 but less than 0.1290.

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

Accepted Answer

The answer of Smith pays $950 for an investment that...

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

Accepted Answer

The answer of Terms of a loan: Amount of loan...

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

Accepted Answer

The present value of the annuity is calculated by considering the increasing payments for the first 10 years and decreasing payments for the next 10 years, discounted at the given interest rates. The calculations show that the present value falls within the range of $19,000 but less than $19,200.

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

Accepted Answer

The answer of A survival function is defined as follows:...

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

Accepted Answer

To find the rate of mortality (q) at age 40 in the associated single decrement table, we first calculate the total number of people exposed to risk of death, which is the initial population minus half the sum of all decrements (since decrements are uniform over the year). The total decrements are 30 (voluntary terminations) + 20 (involuntary terminations) + 10 (disability retirements) + 12 (deaths) = 72. Half of this is 36, so the number exposed to risk is 1500 - 36 = 1464. The number of deaths is 12, so q = 12 / 1464 = 0.008196721, which falls in the range of 0.00815 but less than 0.00817.

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

Accepted Answer

The answer of The market value of a fund and...

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

Accepted Answer

The answer of Smith has the option of receiving a...

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?

Accepted Answer

The maximum annual annuity Smith can receive in the form of a qualified joint and 100% survivor annuity is $50,000 because the plan provides the qualified joint and 100% survivor annuity on a fully subsidized basis.

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?

Accepted Answer

Under ERISA and the Internal Revenue Code, loans from a plan to a plan sponsor are generally considered prohibited transactions, regardless of the repayment terms or interest rates.

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?

Accepted Answer

Under ERISA section 4010, reporting is required for any plan year in which the aggregate unfunded vested benefits of all plans maintained by the sponsor exceed $50 million, considering the plans collectively. Here, the total unfunded vested benefits are $63,000,000 ($13,000,000 from Plan A + $50,000,000 from Plan B), exceeding the $50 million threshold.

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?

Accepted Answer

The amendment can take effect on 3/1/2012 because the AFTAP is at least 60%, allowing benefit increases to take effect without additional funding.

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?

Accepted Answer

Plan assets can be returned to the plan sponsor not only upon plan termination but also in the form of a refund of excess contributions to correct a mistake or to adjust for overfunding, under specific conditions and regulations.

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?

Accepted Answer

Under a 7-year graded vesting schedule, an employee must work for 7 years to become 100% vested. The employee worked from 2002 to 2005 and then from 2009 to 2012, totaling 8 years, but with a break in service that might affect the vesting calculation depending on plan specifics not provided.

Quiz 1: Enrolled Actuary

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 ?

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 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 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?

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?