EA-1 Examination Questions
Spring, 2001
Question 1 (4
points)
Selected
values: 1000d(m) =
85.256
1000d(2m) =
85.715
In what
range is 1000i(3m)?
[A] Less than 86.000
[B] 86.000 but less than 86.400
[C] 86.400 but less than 86.800
[D] 86.800 but less than 87.200
[E] 87.200 or more
Question 2 (2
points)
A loan of
$1,800 is to be repaid by a single payment of $2,420.80 two years after the
date of the loan. The terms of the loan
are quoted using a nominal annual interest rate of 15%.
In what
range is the frequency of compounding?
[A] monthly
[B] every two months
[C] quarterly
[D] semiannually
[E] annually
Question 3 (4
points)
Amount of
a loan: $100,000.
Number of
originally scheduled level annual repayments: 30.
Time of
first repayment: One year from the date of the loan.
Additional
payments made with the 5th and 10th scheduled repayments:
$5,000 each.
Effective
annual interest rate: 6%.
Subsequent
to the two additional payments, the loan continues to be repaid by annual
repayments of the original size, plus a smaller final repayment one year after
the last full repayment.
In what range is the total amount
of interest saved due to the two additional payments?
[A] Less than $23,500
[B] $23,500 but less than $23,600
[C] $23,600 but less than $23,700
[D] $23,700 but less than $23,800
[E] $23,800 or
more
Question 4 (4
points)
Date of a
loan: 1/1/2001.
Amount of
loan: $100,000.
Frequency of
repayments: Quarterly.
Date of
first repayment: 3/31/2001.
Number of
repayments: 120.
Amount of
each of the first 110 repayments: $3,100.
Amount of
each of the last 10 repayments: Initial
repayment of $X, then doubling every quarter thereafter.
Interest
rate: 12% per year, compounded quarterly.
In what
range is the amount of the final repayment?
[A] Less than $6,000
[B] $6,000 but less than $12,000
[C] $12,000 but less than $18,000
[D] $18,000 but less than $24,000
[E] $24,000 or more
Question 5 (5 points)
On 1/1/2002, Smith contributes
$2,000 into a new savings account that earns 5% interest, compounded
annually. On each January 1 thereafter,
he makes another deposit that is 97% of the prior deposit. This continues until he has made 20 deposits
in all.
On each January 1 beginning on
1/1/2025, Smith makes annual withdrawals.
There is to be a total of 25 withdrawals, with each withdrawal 4% more
than the prior withdrawal, and the 25th withdrawal exactly depletes
the account.
In what range is the sum of the
withdrawals made on 1/1/2025 and 1/1/2026?
[A] Less than
$5,410
[B] $5,410 but
less than $5,560
[C] $5,560 but
less than $5,710
[D] $5,710 but
less than $5,860
[E] $5,860 or
more
Question 6 (5 points)
Amount of a loan: $25,000.
Term of loan: 8 years.
Loan repayments: Quarterly, at the
end of each quarter.
Interest rate: 8% per year,
compounded semiannually.
The 11th and 12th
scheduled repayments are not made.
The loan is renegotiated
immediately after the due date of the 12th (2nd missed)
scheduled repayment with the following provisions:
13th
(1st renegotiated) scheduled repayment: $X.
14th
through 32nd repayments:
Each even-numbered repayment is $200 greater than the
immediately preceding (odd-numbered) repayment.
Each odd-numbered repayment is
equal to the immediately preceding even-numbered repayment.
The loan is to be completely
repaid over the original term.
In what range is X?
[A] Less than $250
[B] $250 but less than $255
[C] $255 but less than $260
[D] $260 but less than $265
[E] $265 or more
Question 7
(3 points)
Repayment schedule for a loan:
End
of Each Odd Numbered Year Amount
of Repayment
1
$100
3
$300
5
$500
. .
. .
X $100X
. .
. .
25 $2500
Interest rate: 6% per year,
compounded annually.
A is the total of the payments to
be made after the 15th year.
B is the present value of the
remaining payments as of the beginning of the 16th year.
In what range is A minus B?
[A] Less than $3,120
[B] $3,120 but less than $3,150
[C] $3,150 but less than $3,180
[D] $3,180 but less than $3,210
[E] $3,210 or more
Question 8 (3 points)
Date of a loan: 1/1/2001.
Date of first repayment:
12/31/2001.
Frequency of repayments: Annually.
Term of loan: 4 years.
Amount of each repayment: $1,000.
The sum of the principal
repayments in years one and two is equal to 10v2 times the sum of
the interest repayments in years three and four.
In what range is v?
[A] Less than 0.930
[B] 0.930 but less than 0.935
[C] 0.935 but less than 0.940
[D] 0.940 but less than 0.945
[E] 0.945 or more
Question 9 (2 points)
Amount of a loan: $1,000.
Date of loan: 1/1/2001.
Term of loan: 30 years.
Date of first repayment: 1/1/2004.
Frequency of repayments: Every 3
years.
Interest rate: 4% per year,
compounded annually.
In what range is the principal
repaid in the fifth repayment?
[A] Less than $85
[B] $85 but less than $91
[C] $91 but less than $97
[D] $97 but less than $103
[E] $103 or more
Question 10 (3 points)
Issue date of a bond: January 1,
1994.
Term of bond: 15 years.
Par value of bond: $10,000.
Coupons: 8% per annum, paid on
June 30 and December 31.
Amortized value on July 1, 2001:
$13,741.11.
Amortized value on January 1,
2002: $13,629.67.
In what range is the redemption amount to be paid at
maturity?
[A] Less than
$11,680
[B] $11,680 but
less than $11,750
[C] $11,750 but
less than $11,820
[D] $11,820 but
less than $11,890
[E] $11,890 or more
Question 11 (2 points)
Issue date
of a bond: January 1, 2001.
Coupon
dates: December 31, 2002 and every two
years thereafter, with the final payment on December 31, 2010.
Coupon
amount: $60 each.
Investor’s
yield: 8% per annum.
Price of
the bond at issue: $691.49.
Amortized
value on January 1, 2005: $A.
Amortized
value on January 1, 2007: $B.
In what range is the absolute
value of ($A - $B)?
[A] Less than $63
[B] $63 but less than $66
[C] $66 but less than $69
[D] $69 but less than $72
[E] $72 or more
Question 12 (4 points)
A $200,000, 30-year variable rate
mortgage loan is obtained. The first
monthly payment is due one month from the date of the loan. At the time the loan is obtained, the interest
rate is 7.0%, compounded monthly.
On the second anniversary of the
loan, the interest rate is increased to 7.5%, compounded monthly.
On the fourth anniversary of the
loan, the interest rate is increased to 8.0%, compounded monthly, and remains
fixed for the remainder of the mortgage repayment period.
In what range is the total interest paid on the loan?
[A] Less than
$310,000
[B] $310,000 but
less than $314,000
[C] $314,000 but
less than $318,000
[D] $318,000 but
less than $322,000
[E] $322,000 or
more
Question 13 (2 points)
Purchase date of a perpetuity:
1/1/2001.
Date of first payment: 12/31/2001.
Frequency of payments: Annual.
Amount of each payment: $1.00.
Interest rate: 6% per year,
compounded annually.
In what range is the absolute value of the difference between
the modified duration of the perpetuity and the present value of the
perpetuity?
[A] Less than
0.20
[B] 0.20 but
less than 0.40
[C] 0.40 but
less than 0.60
[D] 0.60 but
less than 0.80
[E] 0.80 or more
Question 14 (5 points)
Consider the following 3
portfolios:
Portfolio
A: 4-year bonds with 7% annual
coupons.
5-year
zero-coupon bonds.
Portfolio
B: 3-year bonds with 7% annual
coupons.
5-year
zero-coupon bonds.
Portfolio
C: 4-year zero-coupon bond with a
maturity value of $10,000.
All bonds yield 7%.
The amount of each type of bond
within a given portfolio is selected such that all three portfolios have the
same present value and the same modified duration.
$X = the amount invested in 5-year
zero-coupon bonds in Portfolio A.
$Y = the amount invested in 5-year
zero-coupon bonds in Portfolio B.
In what range is the absolute
value of ($X - $Y)?
[A] Less than $2,000
[B] $2,000 but less than $2,300
[C] $2,300 but less than $2,600
[D] $2,600 but less than $2,900
[E] $2,900 or more
Question 15 (2 points)
A 12-year annual annuity has its
first payment of $10,000 due one year from purchase. Subsequent payments will be indexed to the excess of the
percentage increase in the Consumer Price Index (CPI) over 3%.
Interest rate: 8% per year,
compounded annually.
$X = the present value of the
annuity if the constant rate of increase in the CPI is 6%.
$Y = the present value of the
annuity if the constant rate of increase in the CPI is 4%.
In what range is the absolute
value of ($X minus $Y)?
[A] Less than $7,745
[B] $7,745 but less than $7,925
[C] $7,925 but less than $8,105
[D] $8,105 but less than $8,285
[E] $8,285 or more
Question 16 (4 points)
Deaths are uniformly distributed
over [0,100]. The interest rate is 6%
compounded annually.
In what range is $100a60?
[A] Less than $1,000
[B] $1,000 but less than $1,005
[C] $1,005 but less than $1,010
[D] $1,010 but less than $1,015
[E] $1,015 or more
Question 17 (3 points)
Interest rate: 7% per year,
compounded annually.
l105+t = (950)(1 -
0.2t), 0 £ t £ 5
Smith is currently age 105. If she survives until age 106, she will
become entitled to a two-year certain and life annuity that pays $1,000 at the
end of each year.
$X is the present value at Smith’s
current age of this annuity.
In what range is $X?
[A] Less than $1,490
[B] $1,490 but less than $1,600
[C] $1,600 but less than $1,710
[D] $1,710 but less than $1,820
[E] $1,820 or more
Question 18 (3 points)
Current age of a mortgagee: 57.
Frequency of level mortgage
payments: Annual, at the end of each year.
Remaining mortgage amount:
$50,000.
Remaining mortgage term: 3 years.
Interest rate: 5% per year,
compounded annually.
The mortgage is insured by the
purchase of a 3-year decreasing term insurance policy with a death benefit
equal to the mortgage balance at the end of the year of death.
Selected values:
x lx
56
9604
57
9574
58
9541
59
9505
60
9467
61
9424
In what range is the current
present value of the insurance benefit?
[A] Less than $350
[B] $350 but less than $360
[C] $360 but less than $370
[D] $370 but less than $380
[E] $380 or more
