Problem 4-13
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.)
a. $800 per
year for 10 years at 8%.
$
b. $400 per
year for 5 years at 4%.
$
c. $800 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.
d. $800 per
year for 10 years at 8%.
$
e. $400 per
year for 5 years at 4%.
$

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Problem 4-6
Future Value: Ordinary Annuity versus Annuity Due
What’s the future
value of a 4%, 4-year ordinary annuity that pays $500 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.
$

Problem 4-11
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 HP-12C, 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 HP-10B gives the correct answer.]
a. 6%.
year(s)
b. 10.1%.
year(s)
c. 16%.
year(s)
d.
100%.
year(s)

Problem 4-4
Number of Periods of a Single Payment
If you deposit money today in an
account that pays 5.2% annual interest, how long will it take to double your
money? Round your answer to the nearest whole.
years

Problem 4-7
Present and Future Value of an Uneven Cash Flow Stream
An investment will pay $200 at the
end of each of the next 3 years, $400 at the end of Year 4, $600 at the end of
Year 5, and $800 at the end of Year 6. If other investments of equal risk earn
4% 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.
$

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.

Q8
A $150,000 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 higher if the interest rate were lower.

d.
The proportion of each payment that represents interest versus repayment of
principal would be higher if the interest rate were higher.

e.
The proportion of interest versus principal repayment would be the same for
each of the 7 payments

Q9
Your bank account pays a 6% nominal
rate of interest. The interest is compounded quarterly. Which of the following
statements is CORRECT?

a.
The periodic rate of interest is 1.5% and the effective rate of interest is
greater than 6%.

b.
The periodic rate of interest is 3% and the effective rate of interest is
6%.

c.
The periodic rate of interest is 1.5% and the effective rate of interest is
3%.

d.
The periodic rate of interest is 6% and the effective rate of interest is
also 6%.

e.
The periodic rate of interest is 6% and the effective rate of interest is
greater than 6%

Problem 4-28
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 $875 each. Your money is now invested in a bank that pays an 6%
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 4-30
Loan Amortization
Your company is planning to borrow
$2,000,000 on a 7-year, 11%, 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.
%

Problem 4-15
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 $700 and promise to pay back $728 at the end
of 1 year.
%You lend $700 and receive a promise to be paid $728 at
the end of 1 year.
%You borrow $95,000 and promise to pay back $156,788 at
the end of 11 years.
%You borrow $8,000 and promise to make payments of
$2,444.9 at the end of each year for 4 years.
%

Problem 4-19
Effective versus Nominal Interest Rates

Universal Bank pays 4% interest,
compounded annually, on time deposits. Regional Bank pays 3%, compounded
quarterly.
Based on effective interest rates, in which bank would
you prefer to deposit your money?

I. You are indifferent between the banks and your decision will be
based upon which one offers you a gift for opening an account.
II. You would choose Universal Bank because its EAR (or EFF%) is
higher.
III.You would choose Regional Bank because its nominal interest
rate is higher.
IV.You would choose Universal Bank because its nominal interest
rate is higher.
V. You would choose Regional Bank because its EAR (or EFF%) 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 (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.
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 Universal 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 Universal 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 think there is a high probability that you will make 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 (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.

Problem 4-24
Required Lump-Sum Payment
To complete your last year in
business school and then go through law school, you will need $20,000 per year
for 4 years, starting next year (that is, you will need to withdraw the first
$20,000 one year from today). Your rich uncle offers to put you through school,
and he will deposit in a bank paying 6.44% interest a sum of money that is
sufficient to provide the 4 payments of $20,000 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.
$