Problem 47
Present and Future Value of an Uneven Cash Flow Stream
An investment will pay $100 at the
end of each of the next 3 years, $400 at the end of Year 4, $500 at the end of
Year 5, and $800 at the end of Year 6. If other investments of equal risk earn
9% annually, what is its present value? Round your answer to the nearest cent.
$
What is its future value? Round your
answer to the nearest cent.
$
Problem 424
Required LumpSum Payment
To complete your last year in
business school and then go through law school, you will need $15,000 per year
for 4 years, starting next year (that is, you will need to withdraw the first
$15,000 one year from today). Your rich uncle offers to put you through school,
and he will deposit in a bank paying 6.51% interest a sum of money that is
sufficient to provide the 4 payments of $15,000 each. His deposit will be made
today.
 How large must the deposit be? Round your answer to the
nearest cent.
$  How much will be in the account immediately after you
make the first withdrawal? Round your answer to the nearest cent.
$
How much will be in the account immediately after you make the last
withdrawal? Round your answer to the nearest cent.
$
Problem 415
Effective Rate of Interest
Find the interest rate (or rates of
return) for each of the following situations. Round your answers to two decimal
places.
 You borrow $650 and promise to pay back $676 at the end
of 1 year.
%  You lend $650 and receive a promise to be paid $676 at
the end of 1 year.
%  You borrow $70,000 and promise to pay back $137,648 at
the end of 8 years.
%  You borrow $10,000 and promise to make payments of
$3,550 at the end of each year for 3 years.
%
4. A $150,000
loan is to be amortized over 7 years, with annual endofyear payments. Which
of these statements is CORRECT?









e.
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5. If you deposit money today in an account that pays 5.4% annual interest,
how long will it take to double your money? Round your answer to the nearest
whole.
years
Problem 431
Nonannual Compounding
 It is now January 1. You plan to make a total of 5
deposits of $400 each, one every 6 months, with the first payment being
made today. The bank pays a nominal interest rate of 12% but uses
semiannual compounding. You plan to leave the money in the bank for 15
years. How much will be in your account after 15 years? Round your answer
to the nearest cent.
$  You must make a payment of $1,981.76 in 10 years. To
get the money for this payment, you will make 5 equal deposits, beginning
today and for the following 4 quarters, in a bank that pays a nominal
interest rate of 6% with quarterly compounding. How large must each of the
5 payments be? Round your answer to the nearest cent.
$
Problem 430
Loan Amortization
Your company is planning to borrow $2,250,000 on a 3year, 12%, annual
payment, fully amortized term loan. What fraction of the payment made at the
end of the second year will represent repayment of principal? Round your answer
to two decimal places.
Which of the following statements regarding
a 30year monthly payment amortized mortgage with a nominal interest rate of
10% is CORRECT?









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QYour bank account pays a 6% nominal rate of interest. The
interest is compounded quarterly. Which of the following statements is CORRECT?









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Problem 411
Time for a Lump Sum to Double
To the next whole year, how long
will it take $200 to double if it is deposited and earns the following rates?
Round your answers up to the next highest year. [Notes: (1) If you are
using a financial calculator, you can enter the known values and then press the
appropriate key to find the unknown variable. Then, without clearing the TVM
register, you can “override” the variable that changes by simply
entering a new value for it and then pressing the key for the unknown variable
to obtain the second answer. This procedure can be used in parts b and d, and
in many other situations, to see how changes in input variables affect the
output variable.) (2) This problem cannot be solved exactly with some financial
calculators. For example, if you enter PV = 200, PMT = 0, FV = 400, and I = 7
in an HP12C, and then press the N key, you will get 11 years. The correct
answer is 10.2448 years, which rounds to 10, but the calculator rounds up.
However, the HP10B gives the correct answer.]
 4.1%.
year(s)  10%.
year(s)  17.3%.
year(s)  100%.
year(s)
Problem 428
PV and Effective Annual Rate
Assume that you inherited some
money. A friend of yours is working as an unpaid intern at a local brokerage firm,
and her boss is selling securities that call for 4 payments of $50 (1 payment
at the end of each of the next 4 years) plus an extra payment of $1,000 at the
end of Year 4. Your friend says she can get you some of these securities at a
cost of $1,050 each. Your money is now invested in a bank that pays an 12%
nominal (quoted) interest rate but with quarterly compounding. You regard the
securities as being just as safe, and as liquid, as your bank deposit, so your
required effective annual rate of return on the securities is the same as that
on your bank deposit. You must calculate the value of the securities to decide
whether they are a good investment. What is their present value to you? Round
your answer to the nearest cent.
$
Problem 413
Present Value of an Annuity
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Find the present value of the
following ordinary annuities. Round your answers to the nearest cent. (Notes:
If you are using a financial calculator, you can enter the known values and
then press the appropriate key to find the unknown variable. Then, without
clearing the TVM register, you can “override” the variable that
changes by simply entering a new value for it and then pressing the key for the
unknown variable to obtain the second answer. This procedure can be used in
many situations, to see how changes in input variables affect the output
variable. Also, note that you can leave values in the TVM register, switch to
“BEG,” press FV, and find the FV of the annuity due.)
 $400 per year for 10 years at 6%.
$  $200 per year for 5 years at 3%.
$  $400 per year for 5 years at 0%.
$
Now rework parts a, b, and c
assuming that payments are made at the beginning of each year; that is, they
are annuities due.
 $400 per year for 10 years at 6%.
 $
 $200 per year for 5 years at 3%.
$  $400 per year for 5 years at 0%.
$
Universal Bank pays 3% interest,
compounded annually, on time deposits. Regional Bank pays 2%, compounded
quarterly.
 Based on effective interest rates, in which bank would
you prefer to deposit your money?I. You would choose Regional Bank because its EAR (or EFF%) is
higher.
II. You would choose Regional Bank because its nominal interest
rate is higher.
III.You are indifferent between the banks and your decision will
be based upon which one offers you a gift for opening an account.
IV.You would choose Universal
Bank because its EAR (or EFF%) is higher.
V. You would choose Universal Bank because its nominal interest
rate is higher.  Could your choice of banks be influenced by the fact
that you might want to withdraw your funds during the year as opposed to
at the end of the year? In answering this question, assume that funds must
be left on deposit during the entire compounding period in order for you
to receive any interest.I. If funds must be left on deposit until the end of the
compounding period (3 months for Universal Bank and 1 year for Regional
Bank), and you think there is a high probability that you will make a
withdrawal during the year, then Universal Bank might be preferable.
II. If funds must be left on
deposit until the end of the compounding period (1 year for Universal Bank
and 3 months for Regional Bank), and you think there is a high probability
that you will make a withdrawal during the year, then Regional Bank might
be preferable.
III.If funds must be left on deposit until the end of the
compounding period (3 months for Universal Bank and 1 year for Regional
Bank), and you think there is a high probability that you will make a
withdrawal during the year, then Regional Bank might be preferable.
IV.If funds must be left on deposit until the end of the
compounding period (1 year for Universal Bank and 3 months for Regional
Bank), and you have no intentions of making a withdrawal during the year,
then Regional Bank might be preferable.
V. If funds must be left on deposit until the end of the
compounding period (1 year for Universal Bank and 3 months for Regional
Bank), and you think there is a high probability that you will make a
withdrawal during the year, then Universal Bank might be preferable.
Problem 46
Future Value: Ordinary Annuity versus Annuity Due
What’s the future value of a 4%,
9year ordinary annuity that pays $700 each year? Round your answer to the
nearest cent.
$
If this were an annuity due, what
would its future value be? Round your answer to the nearest cent.
$
Q A $50,000 loan is to be amortized
over 7 years, with annual endofyear payments. Which of these statements is
CORRECT?








