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EA-1(A) Examination Questions

Spring, 1997

Question 1

Market value of a pension fund:

Date Value Before Cash Flow

01/0l/97 $1,000,000

07/0l/97 1,030,000

X 1,025,000

12/31/97 1,150,000

Total cash flow in fund in 1997:

Benefit

Date Contributions Payments

7/l/97 $ 0 $50,000

X 100,000 0

The time-weighted and dollar-weighted rates of return for the fund are equal.

In what range is X?

[A] Before 8/l/97

[B] 8/l/97 to 8/31/97

[C] 9/l/97 to 9/30/97

[D] 10/l/97 to 10/31/97

[E] 11/1/97 or after

Question 2

Date of a loan: 1/l/97.

Date of first repayment: 1/31/97.

Frequency of repayments: Monthly.

Number of repayments: 36 months.

Amount of each repayment: $100.

Total interest paid in final 12 repayments: $109.20.

In what range is the total interest paid in the middle 12 repayments?

[A] Less than $280

[B] $280 but less than $290

[C] $290 but less than $300

[D] $300 but less than $310

[E] $310 or more

Question 3

Date of a loan: 1/l/92.

Amount of loan: $100,000.

Date of first repayment: 1/31/92.

Frequency of repayments: Monthly.

Number of repayments: 360.

Interest rate: 10% per year, compounded monthly.

The loan is refinanced on 1/l/97 at a revised interest rate of 9% per year, compounded monthly, with the number of remaining monthly repayments reduced to 180.

In what range is the reduction, due to the refinancing, in the total interest payments over the life of the loan?

[A] Less than $80,000

[B] $80,000 but less than $85,000

[C] $85,000 but less than $90,000

[D] $90,000 but less than $95,000

[E] $95,000 or more

Question 4

Terms of a loan:

Date of loan: 1/l/97.

Amount of loan: $200,000.

Interest rate: 9% per year, compounded monthly.

Date of first scheduled repayment: 1/31/97.

Frequency of scheduled repayments: Monthly.

Amount of each scheduled repayment: $P.

Number of scheduled repayments: 360.

The borrower makes additional repayments as follows:

Frequency of additional repayments: Each 12/31.

Amount of additional repayments: $P.

In what range is the reduction in the number of scheduled repayments due to the additional repayments?

[A] Less than 83

[B] 83 but less than 87

[C] 87 but less than 91

[D] 91 but less than 95

[E] 95 or more

Question 5

Data for two funds:

Fund A Fund B

Interest/discount rate for first 10 years i⁽⁴⁾ = 6% d⁽¹²⁾= 9%

Discount/interest rate for second 10 years d⁽⁴⁾ = 9% i⁽¹²⁾= 12%

Initial amount in fund $W $X

Amount in fund at end of 20 years $Y $Z

There are no contributions to or withdrawals from either fund.

$W + $X = $10,000

$Y + $Z = $57,186

In what range is $Y?

[A] Less than $27,500

[B] $27,500 but less than $28,400

[C] $28,400 but less than $29,300

[D] $29,300 but less than $30,200

[E] $30,200 or more

Question 6

Date of a loan: 1/1/97.

Amount of loan: $X.

Date of first repayment: 12/31/97.

Frequency of repayments: Annually.

Number of repayments: 16.

Interest rate: 7% per year, compounded annually.

Amount of each repayment:

First year: $100.

Next 9 years: $200 greater than the prior year’s amount.

Final 6 years: $300 less than the prior year’s amount.

In what range is $X?

[A] Less than $8,300

[B] $8,300 but less than $8,400

[C] $8,400 but less than $8,500

[D] $8,500 but less than $8,600

[E] $8,600 or more

Question 7

Date of a loan: 1/l/97.

Amount of loan: $1,000,000.

Date of first repayment: 1/31/97.

Type and frequency of repayments: Level and monthly.

Number of repayments: 360.

Interest rate for first 15 years: 7% per year, compounded annually.

Interest rate for last l5 years: 11% per year, compounded annually.

In what range is the amount of interest paid in the 204th repayment?

[A] Less than $5,120

[B] $5,120 but less than $5,240

[C] $5,240 but less than $5,360

[D] $5,360 but less than $5,480

[E] $5,480 or more

Question 8

As of 1/l/97, a portfolio of assets consists of the following:

(A) An annuity certain with 20 annual payments of $2,000 beginning on 12/31/2007.

(B) A $10,000 zero coupon bond maturing on 12/31/2001.

Interest rate: 8% per year, compounded annually.

In what range is the modified duration of the portfolio as of 1/l/97?

[A] Less than 10.70

[B] 10.70 but less than 11.20

[C] 11.20 but less than 11.70

[D] 11.70 but less than 12.20

[E] 12.20 or more

Question 9

Face amount of a bond: $1,000.

Coupon rate: 7% per year, payable semiannually on each 6/30 and 12/31.

Amortized value of bond as of 6/30/97 (before payment of coupon): $939.33.

Amortized value of bond as of 12/31/97 (before payment of coupon): $943.78.

In what range is the annual effective yield rate for the bond?

[A] Less than 8.00%

[B] 8.00% but less than 8.25%

[C] 8.25% but less than 8.50%

[D] 8.50% but less than 8.75%

[E] 8.75% or more

Question 10

Date of first payment of a perpetuity: 1/l/97.

Amount of each payment:

Interest rate: 25% per year, compounded annually.

In what range is the present value of the perpetuity as of 1/l/97?

[A] Less than $70

[B] $70 but less than $90

[C] $90 but less than $110

[D] $110 but less than $130

[E] $130 or more

Question 11

Frequency of deposits to a savings account: Monthly.

Date of first deposit: 1/31/81.

Amount of each deposit: $25 each month in first year, increasing each January 31 thereafter by 12% over the monthly amount for the prior year.

Interest rate: 12% per year, compounded monthly.

In what range is the value of the savings account as of 1/l/99?

[A] Less than $40,300

[B] $40,300 but less than $40,700

[C] $40,700 but less than $41,100

[D] $41,100 but less than $41,500

[E] $41,500 or more

Question 12

Type of insurance policy: Endowment at age 65.

Death benefit: $10,000, payable at end of year of death.

Issue age: 45.

Net annual premium: $350.

Selected commutation functions:

D₆₄ = 12,196 D₆₅ = 11,240

The final premium is not paid, and the reserve at the end of the 19th year is used to provide extended term insurance of $10,000 for the final year plus a pure endowment at the end of that year.

In what range is the amount of the pure endowment?

[A] Less than $9,615

[B] $9,615 but less than $9,625

[C] $9,625 but less than $9,635

[D] $9,635 but less than $9,645

[E] $9,645 or more

Question 13

A single premium annuity provides $1,000 at the end of each year if at least one of Smith or Brown is alive and under age 18.

Age of Smith on annuity purchase date: 10.

Age of Brown on annuity purchase date: 14.

Selected annuity factors:

= 3.28 = 5.78 = 3.22

= 5.68 = 3.12 = 5.53

In what range is the net single premium for the annuity?

[A] Less than $5,600

[B] $5,600 but less than $5,700

[C] $5,700 but less than $5,800

[D] $5,800 but less than $5,900

[E] $5,900 or more

Question 14

Selected values from a two decrement (death and withdrawal) table, where each decrement is distributed uniformly over each year of age:

40 100,000

41 93,674

42 87,867

= 213 = .0024

In what range is the probability that an individual aged 40 will withdraw before age 42?

[A] Less than 0.11650

[B] 0.11650 but less than 0.11680

[C] 0.11680 but less than 0.11710

[D] 0.11710 but less than 0.11740

[E] 0.11740 or more

Question 15

A college maintains a stationary population of 15,000 students by annual admissions at ages 18 and 19.

Selected values:

x l_x L_x T_x

18 100,000 97,917 266,668

19 93,750 85,417 168,751

20 75,000 60,417 83,334

21 56,250 22,917 22,917

22 0 0 0

Annual admissions at age 18: 4,000.

In what range is the number of annual admissions at age 19?

[A] Less than 2,250

[B] 2,250 but less than 2,500

[C] 2,500 but less than 2,750

[D] 2,750 but less than 3,000

[E] 3,000 or more

Question 16

Present values of a monthly annuity of $1 payable at the end of each month:

If Smith is alive: $100.

If Brown is alive: $X.

If only Smith is alive: $20.

If only Smith or only Brown is alive: $50.

In what range $X?

[A] Less than $85

[B] $85 but less than $95

[C] $95 but less than $105

[D] $105 but less than $115

[E] $115 or more

Question 17

Terms of an annuity contract:

Date of purchase: 1/l/97.

Date of first payment: 1/l/97.

Amount of each payment: $50.

Frequency of payments: Monthly.

Death benefit: $10,000, payable at end of year of death if death occurs during the first 10 years.

Interest rate: 7% per year, compounded annually.

Annuitant's date of birth: 1/l/32.

Selected commutation functions:

x D_x N_x

65 965 8,872

75 346 2,379

In what range is the net single premium for the annuity contract?

[A] Less than $6,500

[B] $6,500 but less than $7,500

[C] $7,500 but less than $8,500

[D] $8,500 but less than $9,500

[E] $9,500 or more

Question 18

Selected values from a select and ultimate mortality table:

n q_{[x] + n} / q_{x
+ n}

0 .05

1 .65

2 .90

3 or more 1.00

l_x+3 = l_[x]+3

l_x = 1,000 - (10 times x)

In what range is l_{[68]
+ 2} ?

[A] Less than 294

[B] 294 but less than 296

[C] 296 but less than 298

[D] 298 but less than 300

[E] 300 or more

Question 19

Values from a mortality table:

q_x

For 0 £ x £ 35 .01/1.01

For 36 £ x £ 75 .02/1.02

For 76 £ x 1.00

In what range is the curtate expectation of life, e₀?

[A] Less than 48.85

[B] 48.85 but less than 49.35

[C] 49.35 but less than 49.85

[D] 49.85 but less than 50.35

[E] 50.35 or more

Question 20

Type of insurance policy: Whole life.

Death benefit: $1,000, payable at end of year of death.

1000 ₅V₄₀ = 43.46

Selected commutation functions:

x D_x N_x

45 45,482 581,634

46 42,362

In what range is 1000 ₆V₄₀?

[A] Less than 50.00

[B] 50.00 but less than 51.00

[C] 51.00 but less than 52.00

[D] 52.00 but less than 53.00

[E] 53.00 or more