EA-1(A)
Examination Questions
Spring,
1998
Question 1
Initial deposit to a fund: $35,000.
Withdrawal from the fund at the
end of the fourth year: $70,000.
Value of the fund at the end of
the eighth year: $14,000.
No other deposits or withdrawals
were made during the eight-year period.
In what range is the annual rate
of return for the fund during the eight-year period?
[A] Less than 14%
[B] 14% but less than 19%
[C] 19% but less than 24%
[D] 24% but less than 29%
[E] 29% or more
Question 2
Market value of a pension fund on
12/31/96: $60,000.
Contribution made on
10/31/97: $30,000.
Benefit
payments made during 1997: $1,000
per month, paid on the first day of each month.
Using
simple interest:
Dollar-weighted rate of return for
1997: 7.0%.
Expected rate of return for
1997: 6.0%.
In what
range is the investment gain for 1997?
[A] Less than $590
[B] $590 but less than $640
[C] $640 but less than $690
[D] $690 but less than $740
[E] $740 or more
Question 3
At age 30,
Smith established a savings account with an initial deposit of $5,500. He
determined that by making 30 additional annual deposits of $5,500 at each
subsequent age he would accumulate $1,000,000 in the savings account at age 61.
At age 45,
the annual rate of return from age 30 to age 45 is determined to be 9% per
year, compounded annually. If he continues to earn this rate of return to age
61, he will not accumulate $1,000,000 at age 61.
Beginning
with the deposit made at age 45, Smith changes the 16 remaining annual deposits
to $X in order to accumulate $1,000,000 in the savings account at age 61. He
assumes the annual rate of return continues to be 9% per year.
In what
range is $X?
[A] Less than $7,000
[B] $7,000 but less than $8,000
[C] $8,000 but less than $9,000
[D] $9,000 but less than $10,000
[E] $10,000 or more
Question 4
Terms of an annuity:
Date
of first payment: 1/1/99.
Frequency
of payments: Monthly.
Amount of each payment:
First 5 years: $500 per month.
Next 5 years: $650 per month.
Final payment: $10,000
on 1/1/2009.
Interest
rate: 7% per year, compounded annually.
In what
range is the present value of the annuity as of 1/1/98?
[A] Less than $50,500
[B] $50,500 but less than $51,500
[C] $51,500 but less than $52,500
[D] $52,500 but less than $53,500
[E] $53,500 or more
Question 5
Date of a
loan: 1/1/98.
Amount of
loan: $10,000.
Date of
each repayment: 12/31.
Repayment
schedule:
Repayment
Years Amounts
1998 - 2002: $1,000.
2003 - 2004: $0.
2005: $3,000.
2006 - 2011: $1,000.
2012: Balance of
loan.
Interest
rate: 7% per year, compounded annually.
In what
range is the amount of interest included in the repayment to be made in 2007?
[A] Less than $425
[B] $425 but less than $450
[C] $450 but less than $475
[D] $475 but less than $500
[E] $500 or more
Question 6
Total face
amount of a serial bond: $10,000.
Purchase
date: 1/1/98.
Maturity
value: $10,000.
Maturity
date: 12/31/2017.
Coupon
rate: 7% per year, payable on each
12/31.
Yield
rate: 12% per year, compounded
annually.
5% of the
bond will be redeemed at par each 12/31 during the 20-year period 1998 through
2017.
In what
range is the purchase price of the bond on 1/1/98?
[A] Less than $7,500
[B] $7,500 but less than $8,000
[C] $8,000 but less than $8,500
[D] $8,500 but less than $9,000
[E] $9,000 or more
Question 7
Selected
annuity values:
= 14.030
= 52.344
In what
range is the effective annual interest rate?
[A] Less than 5.00%
[B] 5.00% but less than 5.25%
[C] 5.25% but less than 5.50%
[D] 5.50% but less than 5.75%
[E] 5.75% or more
Question 8
Date of a
loan: 1/1/96.
Interest
rate: 18% per year, compounded monthly.
Date of
first repayment: 1/31/96.
Frequency
of repayments: Monthly.
Number of
repayments: 36.
In what
range is the ratio of total interest paid to total principal repaid through the
12/31/97 repayment?
[A] Less than .40
[B] .40 but less than .42
[C] .42 but less than .44
[D] .44 but less than .46
[E] .46 or more
Question 9
Smith is
to repay a loan in 30 annual installments of $10,000 each, beginning one year
after the date of the loan. Immediately after the seventh payment, Smith
borrows an additional $50,000 and combines this loan with the outstanding
balance of the original loan.
Interest
rate for both loans: 7% per year,
compounded annually.
With
respect to the combined loan:
Date of first repayment: 1 year after the loans are combined.
Frequency of repayments: Annually.
Number of repayments: 14.
In what
range is the interest included in the second installment of the combined loan
repayment?
[A] Less than $10,000
[B] $10,000 but less than $10,500
[C] $10,500 but less than $11,000
[D] $11,000 but less than $11,500
[E] $11,500 or more
Question
10
On August
31, 1998, Smith will make a donation to the benefactor fund of his alma mater
to provide for the following:
1. A single four-year tuition scholarship.
