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1. A $50,000 loan is to be
amortized over 7 years, with annual end-of-year payments. Which of these
statements is CORRECT?
a. The annual payments would be
larger if the interest rate were lower.
b. If the loan were amortized
over 10 years rather than 7 years, and if the interest rate were the same in
either case, the first payment would include more dollars of interest under the
7-year amortization plan.
c. The proportion of each payment
that represents interest as opposed to repayment of principal would be lower if
the interest rate were lower.
d. The last payment would have a
higher proportion of interest than the first payment.
e. The proportion of interest
versus principal repayment would be the same for each of the 7 payments.
2. Which of the following
statements is CORRECT?
a. If you have a series of cash
flows, each of which is positive, you can solve for I, where the solution value
of I causes the PV of the cash flows to equal the cash flow at Time 0.
b. If you have a series of cash
flows, and CF0 is negative but each of the following CFs is positive, you can
solve for I, but only if the sum of the undiscounted cash flows exceeds the
cost.
c. To solve for I, one must
identify the value of I that causes the PV of the positive CFs to equal the
absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error
procedure that is easy with a computer or financial calculator but quite
difficult otherwise.
d. If you solve for I and get a
negative number, then you must have made a mistake.
e. If CF0 is positive and all the
other CFs are negative, then you cannot solve for I.
3. Riverside Bank offers to lend
you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal
plus interest) must be repaid at the end of the year. Midwest Bank also offers
to lend you the $50,000, but it will charge an annual rate of 7.0%, with no
interest due until the end of the year. How much higher or lower is the
effective annual rate charged by Midwest versus the rate charged by Riverside?
a. 0.52%
b. 0.44%
c. 0.36%
d. 0.30%
e. 0.24%
4. Steve and Ed are cousins who
were both born on the same day, and both turned 25 today. Their grandfather
began putting $2,500 per year into a trust fund for Steve on his 20th birthday,
and he just made a 6th payment into the fund. The grandfather (or his estate\'s
trustee) will make 40 more $2,500 payments until a 46th and final payment is
made on Steve\'s 65th birthday. The grandfather set things up this way because
he wants Steve to work, not be a \"trust fund baby,\" but he also
wants to ensure that Steve is provided for in his old age.
Until now, the grandfather has
been disappointed with Ed, hence has not given him anything. However, they
recently reconciled, and the grandfather decided to make an equivalent
provision for Ed. He will make the first payment to a trust for Ed today, and
he has instructed his trustee to make 40 additional equal annual payments until
Ed turns 65, when the 41st and final payment will be made. If both trusts earn
an annual return of 8%, how much must the grandfather put into Ed\'s trust
today and each subsequent year to enable him to have the same retirement nest
egg as Steve after the last payment is made on their 65th birthday?
a. $3,726
b. $3,912
c. $4,107
d. $4,313
e. $4,528
5. John and Daphne are saving for
their daughter Ellen\'s college education. Ellen just turned 10 at (t = 0), and
she will be entering college 8 years from now (at t = 8). College tuition and
expenses at State U. are currently $14,500 a year, but they are expected to
increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she
takes longer or wants to go to graduate school, she will be on her own. Tuition
and other costs will be due at the beginning of each school year (at t = 8, 9,
10, and 11).
So far, John and Daphne have
accumulated $15,000 in their college savings account (at t = 0). Their long-run
financial plan is to add an additional $5,000 in each of the next 4 years (at t
= 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each
of the following years, t = 5, 6, and 7. They expect their investment account
to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover
Ellen\'s anticipated college costs?
a. $1,965.21
b. $2,068.64
c. $2,177.51
d. $2,292.12
e. $2,412.76
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