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. $2,412.761
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