PAGE 1

MULTIPLE
CHOICE

1.
Suppose someone offered you your choice of two equally risky annuities, each paying
$5,000 per year for 5 years. One is an annuity due, while the other is a
regular (or deferred) annuity. If you are a rational wealth maximizing investor
which annuity would you choose?

a.
The annuity due.

b.
The deferred annuity.

c.
Either one, because as the problem is set up, they have the same present value.

d. Without information about the appropriate
interest rate, we cannot find the values of the two annuities, hence we cannot
tell which is better.

e. The annuity due; however, if the payments on
both were doubled to $10,000, the deferred annuity would be preferred.

2.
Suppose someone offered you the choice of two equally risky annuities, each
paying $10,000 per year for five years. One is an ordinary (or deferred)
annuity, the other is an annuity due. Which of the following statements is most
correct?

a. The present value of the ordinary annuity must
exceed the present value of the annuity due, but the future value of an
ordinary annuity may be less than the future value of the annuity due.

b. The present value of the annuity due exceeds
the present value of the ordinary annuity, while the future value of the
annuity due is less than the future value of the ordinary annuity.

c. The present value of the annuity due exceeds
the present value of the ordinary annuity, and the future value of the annuity
due also exceeds the future value of the ordinary annuity.

d. If interest rates increase, the difference
between the present value of the ordinary annuity and the present value of the
annuity due remains the same.

e.
Answers a and d are correct.

3.
Which of the following statements is most correct?

a. Other things held constant, an increase in the
number of discounting periods per year increases the present value of a given
annual annuity.

b. Other things held constant, an increase in the
number of discounting periods per year increases the present value of a lump
sum to be received in the future.

c. The payment made each period under an amortized
loan is constant, and it consists of some interest and some principal. The
later we are in the loan's life, the smaller the interest portion of the
payment.

d. There is an inverse relationship between the
present value interest factor of an annuity and the future value interest
factor of an annuity, (i.e., one is the reciprocal of the other).

e.
Each of the statements above is true.

4.
Which of the following is most correct?

a. The present value of a 5-year annuity due will
exceed the present value of a 5-year ordinary annuity. (Assume that both annuities
pay $100 per period and there is no chance of default.)

b. If a loan has a nominal rate of 10 percent,
then the effective rate can never be less than 10 percent.

c. If there is annual compounding, then the
effective, periodic, and nominal rates of interest are all the same.

d.
Answers a and c are correct.

e.
All of the answers above are correct.

5.
Which of the following statements is most correct?

a. An investment which compounds interest
semiannually, and has a nominal rate of 10 percent, will have an effective rate
less than 10 percent.

b. The present value of a three-year $100 annuity
due is less than the present value of a three-year $100 ordinary annuity.

c. The proportion of the payment of a fully
amortized loan which goes toward interest declines over time.

d.
Statements a and c are correct.

e.
None of the answers above is correct.

6.
Which of the following statements is most correct?

a. If an investment has interest compounded
annually, its nominal rate must always equal its effective rate.

b. The present value of a 5-year ordinary annuity
will be greater than the present value of a 5-year annuity due. (Assume that
both annuities pay $100 per period, and that there is no chance of default).

c. In an amortized loan with monthly payments, the
proportion of the payment that goes toward repayment of principal falls
steadily over time.

d.
Answers a and b are correct.

e.
Answers a and c are correct.

7.
Which of the following statements is most correct?

a. The present value of a 5-year ordinary annuity
paying $100 a year will be greater than the present value of a 5-year annuity
due paying $100 a year.

b. If interest is paid more than once a year, then
an investment's effective rate must exceed its nominal rate.

c. On an amortized loan, the percentage of each
payment which goes toward the repayment of principal falls steadily over time.

d.
None of the answers above is correct.

e.
Answers b and c are correct.

8.
Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest rate of 10
percent and monthly compounding. Which of the following statements regarding
his mortgage is most correct?

a.
The monthly payments will decline over time.

b. The proportion of the monthly payment which
represents interest will be lower for the last payment than for the first
payment on the loan.

c. The total dollar amount of principal being paid
off each month gets larger as the loan approaches maturity.

d.
Statements a and c are correct.

e.
Statements b and c are correct.

9. Your subscription to Jogger's World
Monthly is about to run out and you have the choice of renewing it by sending
in the $10 a year regular rate or of getting a lifetime subscription to the
magazine by paying $100. Your cost of capital is 7 percent. How many years
would you have to live to make the lifetime subscription the better buy?
Payments for the regular subscription are made at the beginning of each year.
(Round up if necessary to obtain a whole number of years.)

a.
15 years

b.
10 years

c.
18 years

d. 7 years

e. 8 years

10.
Assume you are to receive a 20-year annuity with annual payments of $50. The
first payment will be received at the end of Year 1, and the last payment will
be received at the end of Year 20. You will invest each payment in an account
that pays 10 percent. What will be the value in your account at the end of Year
30?

a.
$6,354.81

b.
$7,427.83

c.
$7,922.33

d.
$8,591.00

e.
$6,752.46

11.
You are contributing money to an investment account so that you can purchase a house
in five years. You plan to contribute six payments of $3,000 a year--the first
payment will be made today (t = 0), and the final payment will be made five
years from now (t = 5). If you earn 11 percent in your investment account, how
much money will you have in the account five years from now (at t = 5)?

a.
$19,412

b.
$20,856

c.
$21,683

d.
$23,739

e.
$26,350

12.
Your uncle has agreed to deposit $3,000 in your brokerage account at the
beginning of each of the next five years (t = 0, t = 1, t = 2, t = 3 and t =
4). You estimate that you can earn 9 percent a year on your investments. How
much will you have in your account four years from now (at t = 4)? (Assume that
no money is withdrawn from the account until t = 4.)

a.
$13,719.39

b.
$17,954.13

c.
$19,570.00

d.
$21,430.45

e.
$22,436.12

13.
You just put $1,000 in a bank account which pays 6 percent nominal annual
interest, compounded monthly. How much will you have in your account after 3
years?

a.
$1,006.00

b.
$1,056.45

c.
$1,180.32

d.
$1,191.00

e.
$1,196.68

14.
Assume that you can invest to earn a stated annual rate of return of 12
percent, but where interest is compounded semiannually. If you make 20
consecutive semiannual deposits of $500 each, with the first deposit being made
today, what will your balance be at the end of *Year 20*?

a.
$52,821.19

b.
$57,900.83

c.
$58,988.19

d.
$62,527.47

e.
$64,131.50

15.
You have $2,000 invested in a bank account that pays a 4 percent nominal annual
interest with daily compounding. How much money will you have in the account at
the end of July (i.e., in 132 days)? (Assume there are 365 days in each year.)

a.
$2,029.14

b.
$2,028.93

c.
$2,040.00

d.
$2,023.44

e.
$2,023.99

16.
You are interested in saving money for your first house. Your plan is to make
regular deposits into a brokerage account which will earn 14 percent. Your
first deposit of $5,000 will be made today. You also plan to make four
additional deposits at the beginning of each of the next four years. Your plan
is to increase your deposits by 10 percent a year. (That is you plan to deposit
$5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your
account after five years?

a.
$24,697.40

b.
$30,525.00

c.
$32,485.98

d.
$39,362.57

e.
$44,873.90

17.
Assume that your required rate of return is 12 percent and you are given the
following stream of cash flows:

__Year__ __Cash Flow__

0 $10,000

1 15,000

2 15,000

3 15,000

4 15,000

5 20,000

If
payments are made at the end of each period, what is the present value of the
cash flow stream?

a.
$66,909

b.
$57,323

c.
$61,815

d.
$52,345

e.
$62,029

18.
You are given the following cash flows. What is the present value (t = 0) if
the discount rate is 12 percent?

0 12% 1 2
3 4 5 6
Periods

0
1 2,000 2,000 2,000
0 -2,000

a.
$3,277

b.
$4,804

c.
$5,302

d.
$4,289

e.
$2,804

19.
You are given the following cash flow information. The appropriate discount rate
is 12 percent for Years 1-5 and 10 percent for Years 6-10. Payments are
received at the end of the year.

__Year__ __Amount__

1-5
$20,000

6-10
$25,000

What
should you be willing to pay right now to receive the income stream above?

a.
$166,866

b.
$158,791

c.
$225,000

d.
$125,870

e.
$198,433

20. A
project with a 3-year life has the following probability distributions for possible
end-of-year cash flows in each of the next three years:

__Year 1__
__Year 2__
__Year 3__

__Prob__ __Cash Flow__ __Prob__ __Cash Flow__ __Prob__ __Cash Flow__

0.30 $300
0.15 $100 0.25 $200

0.40
500
0.35
200
0.75 800

0.30
700
0.35 600

Using
an interest rate of 8 percent, find the expected present value of these uncertain
cash flows. (Hint: Find the expected cash flow in each year, then evaluate
those cash flows.)

b.
$ 835.42

c.
$1,519.21

d.
$1,580.00

e.
$1,347.61

21.
You just graduated, and you plan to work for 10 years and then to leave for the
Australian "Outback" bush country. You figure you can save $1,000 a
year for the first 5 years and $2,000 a year for the next 5 years. These
savings cash flows will start one year from now. In addition, your family has
just given you a $5,000 graduation gift. If you put the gift now, and your
future savings when they start, into an account which pays 8 percent compounded
annually, what will your financial "stake" be when you leave for
Australia 10 years from now?

a.
$21,432

b.
$28,393

c.
$16,651

d.
$31,148

e.
$20,000

22.
Foster Industries has a project which has the following cash flows:

__t__ __Cash
Flow__

0 -$300.00

1
100.00

2
125.43

3
90.12

4
?

What
cash flow will the project have to generate in the fourth year in order for the
project to have an internal rate of return = 15%?

a.
$ 15.55

b.
$ 58.95

c.
$100.25

d.
$103.10

e.
$150.75

23.
You recently purchased a 20-year investment which pays you $100 at t = 1, $500
at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of each of the
remaining 17 years. The investment cost you $5,544.87. Alternative investments
of equal risk have a required return of 9 percent. What is the annual cash flow
received at the end of each of the final 17 years, that is, what is X?

a.
$600

b.
$625

c.
$650

d.
$675

e.
$700

24.
John Keene recently invested $2,566.70 in a project that is promising to return
12 percent per year. The cash flows are expected to be as follows:

End of
Cash

__ Year __ __Flow__

1 $325

2
400

3 550

4 ?

5 750

6 800

What
is the cash flow at the end of the 4th year?

a.
$1,187

b.
$ 600

c.
$1,157

d.
$ 655

e.
$1,267

25.
An investment costs $3,000 today and provides cash flows at the end of each
year for 20 years. The relevant cost of capital is 10 percent. The projected
cash flows for years 1, 2, and 3 are $100, $200, and $300 respectively. What is
the annual cash flow received for each of the years 4 through 20 (17 years)?
(Assume the same payment for each of these years.)

a.
$285.41

b.
$313.96

c.
$379.89

d.
$417.87

e.
$459.66

26. If
you buy a factory for $250,000 and the terms are 20 percent down, the balance
to be paid off over 30 years at a 12 percent rate of interest on the unpaid
balance, what are the 30 equal annual payments?

a.
$20,593

b.
$31,036

c.
$24,829

d.
$50,212

e.
$ 6,667

27.
Drexel Corporation has been enjoying a phenomenal rate of growth since its
inception one year ago. Currently, its assets total $100,000. If growth
continues at the current rate of 12 percent compounded quarterly, what will
total assets be at the end of 10 quarters?

a.
$142,571

b.
$126,678

c.
$148,016

d.
$136,855

e.
$134,392

28.
If it were evaluated with an interest rate of 0 percent, a 10-year regular
annuity would have a *present value* of $3,755.50. If the *future*

*(compounded)
value* of this
annuity, evaluated at Year 10, is $5,440.22, what effective annual interest
rate must the analyst be using to find the future value?

a. 7%

b. 8%

c. 9%

d.
10%

e.
11%

29.
On January 1, 1993, a graduate student developed a 5-year financial plan which
would provide enough money at the end of her graduate work (January 1, 1998) to
open a business of her own. Her plan was to deposit $8,000 per year for 5
years, starting immediately, into an account paying 10 percent compounded
annually. Her activities proceeded according to plan except that at the end of
her third year (1/1/96) she withdrew $5,000 to take a Caribbean cruise, at the
end of the fourth year (1/1/97) she withdrew $5,000 to buy a used Prelude, and
at the end of the fifth year (1/1/98) she had to withdraw $5,000 to pay to have
her dissertation typed. Her account, at the end of the fifth year, was less
than the amount she had originally planned on by how much?

a.
$15,373

b.
$16,550

c.
$32,290

d.
$38,352

e.
$13,975

30. Suppose
you put $100 into a savings account today, the account pays a nominal annual
interest rate of 6 percent, but compounded semiannually, and you withdraw $100
after 6 months. What would your ending balance be 20 years after the initial
$100 deposit was made?

a.
$226.20

b.
$115.35

c.
$ 62.91

d.
$ 9.50

e.
$ 3.00

31. You have just taken out a 30-year, $120,000
mortgage on your new home. This mortgage is to be repaid in 360 equal
end-of-month installments. If each of the monthly installments is $1,500, what
is the effective annual interest rate on this mortgage?

a.
15.87%

b.
14.75%

c.
13.38%

d.
16.25%

e.
16.49%

32.
You have just borrowed $20,000 to buy a new car. The loan agreement calls for 60
monthly payments of $444.89 each to begin one month from today. If the interest
is compounded monthly, then what is the effective annual rate on this loan?

a.
12.68%

b.
14.12%

c.
12.00%

d.
13.25%

e.
15.08%

33.
You have just taken out a 30-year mortgage on your new home for $120,000. This
mortgage is to be repaid in 360 equal monthly installments. If the stated
(nominal) annual interest rate is 14.75 percent, what is the amount of each of
the monthly installments?

a.
$1,515.00

b.
$1,472.38

c.
$1,493.41

d.
$1,522.85

e.
$1,440.92

34. A
baseball player is offered a 5-year contract which pays him the following
amounts:

Year 1:
$1.2 million

Year
2: 1.6 million

Year
3: 2.0 million

Year
4: 2.4 million

Year
5: 2.8 million

Under
the terms of the agreement all payments are made at the *end* of each year.

Instead
of accepting the contract, the baseball player asks his agent to negotiate a
contract which has a present value of $1 million more than that which has been
offered. Moreover, the player wants to receive his payments in the form of a
5-year annuity due. All cash flows are discounted at 10 percent. If the team
were to agree to the player's terms, what would be the player's annual salary
(in millions of dollars)?

a.
$1.500

b.
$1.659

c.
$1.989

d.
$2.343

e.
$2.500

35.
Your company must make payments of $100,000 each year for 10 years, with the
first payment to be made 10 years from today. To prepare for these payments,
your company must make 10 equal annual deposits into an account which pays a
nominal interest rate of 7 percent, daily compounding (360-day year). Funds
will remain in the account during both the accumulation period (the first 10
years) and the distribution period (the last 10 years), and the same interest
rate will be earned throughout the entire 20 years. The first deposit will be
made immediately. How large must each deposit be?

a.
$47,821.11

b.
$49,661.86

c.
$51,234.67

d.
$52,497.33

e.
$53,262.39

36.
Your lease calls for payments of $500 at the end of each month for the next 12
months. Now your landlord offers you a new 1-year lease which calls for zero
rent for 3 months, then rental payments of $700 at the end of each month for
the next 9 months. You keep your money in a bank time deposit that pays a
nominal annual rate of 5 percent. By what amount would your net worth change if
you accept the new lease? (Hint: Your return *per month* is 5%/12 =
0.4166667%.)

a.
-$509.81

b.
-$253.62

c.
+$125.30

d.
+$253.62

e.
+$509.81

37. Josh
and John (2 brothers) are each trying to save enough money to buy their own
cars. Josh is planning to save $100 from every paycheck (he is paid every 2
weeks). John plans to put aside $150 each month but has already saved $1,500.
Interest rates are currently quoted at 10 percent. Josh's bank compounds
interest every two weeks while John's bank compounds interest monthly. At the
end of 2 years they will each spend all their savings on a car (each brother
buys a car). What is the price of the most expensive car purchased?

a.
$5,744.29

b.
$5,807.48

c.
$5,703.02

d.
$5,797.63

e.
None of the answers above is correct.

38.
An investment pays $100 every six months (semiannually) over the next 2.5 years. Interest, however, is compounded
quarterly, at a nominal rate of 8 percent. What is the future value of the
investment after 2.5 years?

a.
$520.61

b.
$541.63

c.
$542.07

d.
$543.98

e.
$547.49

39.
You have just bought a security which pays $500 every six months. The security
lasts for ten years. Another security of equal risk also has a maturity of ten
years, and pays 10 percent compounded monthly (that is, the nominal rate is 10
percent). What should be the price of the security that you just purchased?

a.
$6,108.46

b.
$6,175.82

c.
$6,231.11

d.
$6,566.21

e.
$7,314.86

40.
You have been offered an investment that pays $500 at the end of every 6 months
for the next 3 years. The nominal interest rate is 12 percent; however,
interest is compounded quarterly. What is the present value of the investment?

a.
$2,458.66

b.
$2,444.67

c.
$2,451.73

d.
$2,463.33

e.
$2,437.56

41. A
ten-year security generates cash flows of $2,000 a year at the end of each of
the next three years (t = 1, 2, 3). After three years, the security pays some
constant cash flow at the end of each of the next six years. (t = 4, 5, 6, 7,
8, 9). Ten years from now (t = 10) the security will mature and pay $10,000.
The security sells for $24,307.85, and has a yield to maturity of 7.3 percent.
What annual cash flow does the security pay for years 4 through 9?

a.
$2,995

b.
$3,568

c.
$3,700

d.
$3,970

e.
$4,296

42.
Your company is planning to borrow $2,500,000 on a 10-year, 9 percent, annual
payment, fully amortized term loan. What fraction of the payment made at the
end of the third year will represent repayment of principal?

a.
29.83%

b.
50.19%

c.
35.02%

d.
64.45%

e.
72.36%

43.
You have just bought a house and have a $125,000, 25-year mortgage with a fixed
interest rate of 8.5 percent with monthly payments. Over the next five years, what
percentage of your mortgage payments will go toward the repayment of principal?

a. 8.50%

b.
10.67%

c.
12.88%

d.
14.93%

e.
17.55%

44.
You have just taken out an installment loan for $100,000. Assume that the loan will
be repaid in 12 equal monthly installments of $9,456 and that the first payment
will be due one month from today. How much of your third monthly payment will
go toward the repayment of principal?

a.
$7,757.16

b.
$6,359.12

c.
$7,212.50

d.
$7,925.88

e.
$8,333.33

45.
The Desai Company just borrowed $1,000,000 for 3 years at a quoted rate of 8
percent, quarterly compounding. The loan is to be amortized in end-of-quarter
payments over its 3-year life. How much interest (in dollars) will your company
have to pay during the second quarter?

a.
$15,675.19

b.
$18,508.81

c.
$21,205.33

d.
$24,678.89

e.
$28,111.66

46.
You have a 30-year mortgage with a nominal annual interest rate of 8.5 percent.
The monthly payment is $1,000. What percentage of your total payments over the
first three years goes toward the repayment of principal?

a.
1.50%

b.
3.42%

c.
5.23%

d.
6.75%

e.
8.94%

47.
You have a $175,000, 30-year mortgage with a 9 percent nominal rate. You make
payments every month. What will be the remaining balance on your mortgage after
5 years?

a.
$ 90,514.62

b.
$153,680.43

c.
$167,790.15

d.
$173,804.41

e.
$174,514.83

48.
You just bought a house and have a $150,000 mortgage. The mortgage is for 30 years
and has a nominal rate of 8 percent (compounded monthly). After 36 payments (3
years) what will be the remaining balance on your mortgage?

a.
$110,376.71

b.
$124,565.82

c.
$144,953.86

d.
$145,920.12

e.
$148,746.95

49.
Your family purchased a house three years ago. When you bought the house you
financed it with a $160,000 mortgage with an 8.5 percent nominal interest rate
(compounded monthly). The mortgage was for 15 years (180 months). What is the
remaining balance on your mortgage today?

a.
$ 95,649

b.
$103,300

c.
$125,745

d.
$141,937

e.
$159,998

50.
You have just taken out a 10-year, $12,000 loan to purchase a new car. This
loan is to be repaid in 120 equal end-of-month installments. If each of the
monthly installments is $150, what is the effective annual interest rate on
this car loan?

a.
6.5431%

b.
7.8942%

c.
8.6892%

d.
8.8869%

e.
9.0438%

ANSWER
KEY FOR TEST - UNTITLED

1.
a. The annuity due.

Annuities

2. c.
The present value of the annuity due exceeds the present value of the ordinary
annuity, and the future value of the annuity due also exceeds the future value
of the ordinary annuity.

Annuities

By
definition, an annuity due is received at the beginning of the year while an
ordinary annuity is received at the end of the year. Because the payments are
received earlier, both the present the future values of the annuity due are
greater than those of the ordinary annuity

3. c.
The payment made each period under an amortized loan is constant, and it
consists of some interest and some principal. The later we are

in
the loan's life, the smaller the interest portion of the payment.

4.
e. All of the answers above are correct.

Time
value concepts

5.
c. The proportion of the payment of a fully amortized loan which goes towards
interest declines over time.

Time
value concepts

Statement
c is correct; the other statements are false. The effective rate of the
investment in statement a is 10.25%. The present value of the annuity due is
greater than the present value of the ordinary annuity.

6.
a. If an investment has interest compounded annually, its nominal rate must
always equal its effective rate.

Miscellaneous
concepts

Statement
a is correct; the other statements are false. The annuity due's cash flows are
received sooner than those of the ordinary annuity.

7.
b. If interest is paid more than once a year, then an investment's effective
rate must exceed its nominal rate.

Miscellaneous
concepts

8.
e. Statements b and c are correct.

Amortization

9.
a. 15 years

PV
of an annuity

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calculator solution:

Inputs:
I = 7; PV = -90; PMT = 10; FV = 0. Output: N = 14.695 ÷ 15 years.

10. b.
$7,427.83

FV
of an annuity

Financial
calculator solution:

*Calculate
FV at Year 20, then take that lump sum forward 10 years to year 30 at 10%.*

Inputs:
N = 20; I = 10; PV = 0; PMT = -50. Output_{Year} Ž™: FV = $2,863.75.

*At
Year 30*

Inputs:
N = 10; I = 10; PV = -2,863.75; PMT = 0.

Output_{Year}
™: FV = $7,427.83.

11.
d. $23,739

FV
of annuity due

There
are a few ways to do this. One way is shown below.

To
get the value at t = 5 of the first 5 payments:

BEGIN
mode

N
= 5

I
= 11

PV
= 0

PMT
= -3,000

FV
= $20,738.58

Now
add on to this the last payment that occurs at t = 5.

$20,728.58
+ $3,000 = $23,738.58 ÷ $23,739.

12. b.
$17,954.13

FV
of annuity due

BEGIN
Mode

N
= 4

I
= 9

PV
= 0

PMT
= -3,000

FV
= $14,954.13.

13.
e. $1,196.68

FV
under monthly compounding

N
= 3 x 12 = 36

I
= 6/12 = 0.5

PV
= -1,000

PMT
= 0

Solve
for FV = $1,196.68.

14.
d. $62,527.47

FV
under semiannual compounding

*Calculate
the FV as of Year 10*

BEGIN
mode, Inputs: N = 20; I = 6; PV = 0; PMT = -500.

Output:
FV = $19,496.36.

*Calculate
the FV as of Year 20 using FV*™ *as the PV*

END
mode, Inputs: N = 20; I = 6; PV = -19,496.36; PMT = 0.

Output:
FV = $62,527.47.

15. a. $2,029.14

FV
under daily compounding

16.
e. $44,873.90

FV
of lump sum and annuity

First,
calculate the payment amounts:

PMT™
= $5,000, PMT = $5,500, PMTŽ = $6,050, PMT = $6,655, PMT“ = $7,320.50.

Then,
find the future value of each payment at t = 5:

For
PMT™, N = 5, I = 14, PV = -5,000, PMT = 0; thus, FV = $9,627.0729.

Similarly,
for PMT, FV = $9,289.2809, for PMTŽ, FV = $8,963.3412, for PMT, FV =
$8,648.8380, and for PMT“, FV = $8,345.3700.

Finally,
summing the future values of the respective payments will give the balance in
the account at t = 5 or $44,873.90.

17. a.
$66,909

PV
of an uneven CF stream

Financial
calculator solution:

*Using
cash flows*

Inputs:
CF™ = 10,000; CF = 15,000; N_{j} = 4 times; CFŽ = 20,000;

I =
12.

Output:
NPV = $66,908.78 ÷ $66,909.

18.
a. $3,277

PV
of an uneven CF stream

Inputs:
CF™ = 0; CF = 1; CFŽ = 2,000; N_{j} = 3 times; CF = 0;

CF“
= -2,000; I = 12.

Output:
NPV = $3,276.615 ÷ $3,277.

19. d. $125,870

PV
of an uneven CF stream

Financial
calculator solution:

*Solve
for PV at time = 0 of $20,000 annuity*

Inputs:
CF™ = 0; CF = 20,000; N_{j} = 5 times; I = 12.

Output:
NPV™ = $72,095.524.

*Solve
for PV at time = 5 of $25,000 annuity using its value at t = 5*

Inputs:
CF™ = 0; CF = 25,000; N_{j} = 5 times; I = 10.

Output:
NPV” = 94,769.669.

*Solve
for PV at time = 0 of $25,000 annuity*

Inputs:
N = 5; I = 12; PMT = 0; FV = -94,769.669.

Output:
PV = $53,774,855.

*Add
the two PVs together*

PV_{Both
annuities} = $72,095.524 + $53,774.855 = $125,870.38 ÷ $125,870.

20.
e. $1,347.61

PV
of uncertain cash flows

Financial
calculator solution:

*Using
cash flows,*

Inputs:
CF™ = 0; CF = 500; CFŽ = 430; CF = 650; I = 8.

Output:
NPV = $1,347.61.

21. d. $31,148

FV
of an uneven CF stream

Financial
calculator solution:

*Solution
using NFV:* (**Note:**
Some calculators do not have net future value function. Cash flows can be grouped
and carried forward or PV can be used; see alternative solution below.)

Inputs:
CF™ = 5,000; CF = 1,000; N_{j} = 5; CFŽ = 2,000; N_{j} = 5; I
= 8.

Output:
NFV = $31,147.79 ÷ $31,148.

*Alternative
solution: Calculate PV of the cash flows, then bring them forward to FV using
the interest rate.*

Inputs:
CF™ = 5,000; CF = 1,000; N_{j} = 5; CFŽ = 2,000; N_{j} = 5; I
= 8.

Output:
PV = $14,427.45.

Inputs:
N = 10; I = 8; PV = -14,427.45.

Output:
FV = $31,147.79 ÷ $31,148.

22. d. $103.10

Value
of missing cash flow

Enter
the first 4 cash flows, enter I = 15, and solve for NPV = $58.945. The future
value of $58.945 will be the required cash flow.

PV
= -58.945; N = 4; I/YR = 15; PMT = 0; solve for FV = $103.10.

23. d. $675

Value
of missing payments

Find
the FV of the price and the first three cash flows at t = 3.

To
do this first find the present value of them.

CF™
= -5,544.87

CF
= 100

CFŽ
= 500

CF
= 750

I
= 9; solve for NPV = -$4,453.15.

N
= 3

I
= 9

PV
= -4,453.15

PMT
= 0

FV
= $5,766.96.

Now
solve for X.

N
= 17

I
= 9

PV
= -5,766.96

FV
= 0

Solve
for PMT = $675.

24. c. $1,157

Value
of missing payment

Find
the present value of each of the cash flows:

PV
of CF = $325/1.12 = $290.18. PV of CFŽ = $400/(1.12)‚ = $318.88.

PV
of CF = $550/(1.12)„ = $391.48. PV of CF” = $750/(1.12)‡ = $425.57.

PV
of CF• = $800/(1.12)ˆ = $405.30. Summing these values you obtain $1,831.41. The
present value of CF“ must then be $2,566.70 - $1,831.41 = $735.29. The value of
CF“ is ($735.29)(1.12)… = $1,157.

25. d. $417.87

Value
of missing payment

The
project's cost should be the PV of the future cash flows. Use the cash flow key
to find the PV of the first 3 years of cash flows.

CF™
= 0, CF = 100; CFŽ = 200, CF = 300, I/YR = 10, NPV = $481.59.

The
PV of the cash flows for years 4 - 20 must be:

$3,000
- $481.59 = $2,518.41.

Take
this amount forward in time 3 years:

N
= 3, I/YR = 10, PV = -2,518.41, PMT = 0, solve for FV = $3,352.00.

This
amount is also the present value of the 17-year annuity.

N
= 17, I/YR = 10, PV = -3,352, FV = 0, solve for PMT = $417.87.

26. c. $24,829

Amortization

Financial
calculator solution:

Inputs:
N = 30; I = 12; PV = -200,000; FV = 0.

Output:
PMT = $24,828.73 ÷ $24,829.

27. e. $134,392

Non-annual
compounding

Financial
calculator solution:

Inputs:
N = 10; I = 3; PV = -100,000; PMT = 0.

Output:
FV = $134,391.64 ÷ $134,392.

28. b.
8%

Effective
annual rate

Financial
calculator solution:

*Calculate
the PMT of the annuity*

Inputs:
N = 10; I = 0; PV = -3,755.50; FV = 0. Output: PMT = $375.55.

*Calculate
the effective annual interest rate*

Inputs:
N = 10; PV = 0; PMT = -375.55; FV = 5,440.22.

Output:
I = 7.999 ÷ 8.0%.

29. b. $16,550

Annuity
value

Financial
calculator solution:

*Calculate
the FV of the withdrawals which is how much her actual account fell short of
her plan.*

END
mode Inputs: N = 3; I = 10; PV =
0; PMT = -5,000.

Output:
FV = $16,550.

Alternative
solution: *Calculate FV of original plan*.

BEGIN
mode Inputs: N = 5; I = 10; PV =
0; PMT = -8,000.

Output:
FV = $53,724.88.

*Calculate
FV of actual deposits less withdrawals, take the difference.*

Inputs:
CF™ = 8,000; CF = 8,000; N_{j} = 2; CFŽ = 3,000; N_{j} = 2;

CF
= -5,000; I = 10.

Output:
NFV = $37,174.80.

Difference:
$53,724.88 - $37,174.80 = $16,550.08.

30. d. $
9.50

FV
of a sum

Inputs:
N = 39; I = 3; PV = -3.00; PMT = 0. Output: FV = $9.50.

31. a. 15.87%

Effective
annual rate

Financial
calculator solution:

*Calculate
periodic rate*

Inputs:
N = 360; PV = -120,000; PMT = 1,500; FV = 0.

Output:
I = 1.235% per period.

*Use
interest rate conversion feature*

Inputs:
NOM% = 1.235 x 12 = 14.82; P/YR = 12.

Output:
EFF% = 15.868% ÷ 15.87%.

32. a. 12.68%

Effective
annual rate

*Calculate
periodic rate and nominal rate*

Inputs:
N = 60; PV = -20,000; PMT = 444.89; FV = 0.

Output:
I = 1.0. NOM% = 1.0% x 12 = 12.00%.

*Use
interest rate conversion feature*

Inputs:
P/YR = 12; NOM% = 12.0. Output: EFF% = EAR = 12.68%.

33. c. $1,493.41

Required
annuity payments

Financial
calculator solution:

Inputs:
N = 360; I = 14.75/12 ÷ 1.2292; PV = -120,000; FV = 0.

Output:
PMT = $1,493.409 ÷ $1,493.41.

34. c. $1.989

Required
annuity payments

Enter
CFs:

CF™
= 0

CF
= 1.2

CFŽ
= 1.6

CF
= 2.0

CF“
= 2.4

CF”
= 2.8

I
= 10%; NPV = $7.2937 million.

$1
+ $7.2937 = $8.2937.

Now,
calculate the annual payments. BEGIN mode

N
= 5; I/YR = 10; PV = -8.2937; FV = 0; PMT = ? + $1.989 million.

35. b. $49,661.86

Annuities
and daily compounding

The
FV of the DEP annuity at T = 10 must be sufficient to make the 10 payments of
$100,000 each.

__Step
1__ Find the PV of the $100,000 payments at
the end of Year 10.

This is a 10-year *annuity due*. What rat do we use? 7% is not

correct, and if we use the periodic rate, that won't work

either in an annuity setup. We want a rate that's consistent

with an *annual* annuity. That means we must use the EAR.

Use the interest conversion feature on your financial

calculator to find EAR = 7.2501%.

P/YR = 360

NOM% = 7

Solve for EFF% = 7.2501%.

Now
find the PV of the annuity:

BEGIN

10
7.2501
100,000 0

³ N
³ ³ I ³ ³ PV ³ ³PMT³ ³FV³

-744,647,80

__Step
2__ Determine the amount of the annuity due
by using the present

value of the $100,000 payments at Year 10 as the future value

of
the annuity due.

BEGIN

10
7.2501
0
744,647.80

³ N
³ ³ I ³ ³ PV ³ ³PMT³ ³FV³

-49,661.86

Deposits of $49,661.86 will
provide the needed funds

36. b. -$253.62

37.
d. $5,797.63

FV
under non-annual compounding

38.
c. $542.07

FV
under quarterly compounding

NOM%
= 8

P/YR
= 4

Solve
for EFF% = 8.2432%.

EFF%
= 8.2432

P/YR
= 2

Solve
for NOM% = 8.08%.

N
= 2.5 x 2 = 5

I
= 8.08/2 = 4.04

PV
= 0

PMT
= -100

PV
= 0

Solve
for FV = $542.07.

39.
b. $6,175.82

PV
under monthly compounding

*Start
by calculating the effective rate on the second security:*

P/YR
= 12

NOM%
= 10

Solve
for EFF% = 10.4713%.

*Then,
convert this effective rate to a semiannual rate:*

EFF%
= 10.4713

P/YR
= 2

NOM%
= 10.2107%.

*Now,
calculate the value of the first security as follows:*

N
= 10 x 2 = 20, I = 10.2107/2 = 5.1054, PMT = 500, FV = 0, thus, PV = -$6,175.82.

40. c. $2,451.73

PV
under non-annual compounding

The
answer is c. First, find the effective annual rate for a nominal rate of 12%
with quarterly compounding: P/YR = 4, NOM% = 12, and EFF% = ? = 12.55%. In
order to discount the cash flows properly, it is necessary to find the nominal
rate with semiannual compounding that corresponds to the effective rate
calculated above. Convert the effective rate to a semiannual nominal rate as
P/YR = 2, EFF% = 12.55, and NOM% = ? = 12.18%. Finally, find the PV as N = 2 x
3 = 6, I = 12.18/2 = 6.09, PMT = 500, FV = 0, and PV = ? = -$2,451.73.

41. c. $3,700

Value
of missing payments

There
are several different ways of doing this. One way is:

Find
the future value of the first three years of the investment at Year 3.

N
= 3

I
= 7.3

PV
= -24,307.85

PMT
= 2,000

FV
= $23,580.68.

Find
the value of the final $10,000 at Year 3.

N
= 7

I
= 7.3

PMT
= 0

FV
= 10,000

PV
= -$6,106.63.

Add
the two Year 3 values (remember to keep the signs right).

$23,580.68
+ -$6,106.63 = $17,474.05.

Now
solve for the PMTs over years 4 through 9 (6 years) that have a PV of
$17,474.05.

N
= 6

I
= 7.3

PV
= -17,474.05

FV
= 0

PMT
= $3,700.00.

42.
b. 50.19%

Amortization

*Calculate
the principal portion of PMT using amortization function:*(**Note:** The steps below are
specific to the Hewlett-Packard 17B II but the basic steps generalize to a
variety of calculators.)

Inputs:
N = 10; I = 9; PV = -2,500,000. Output: PMT = $389,550.22.

Inputs:
[AMORT], #P = 3, [NEXT] or [AMORT].

Output:
[=] or [PRIN] = 195,502.12.

Principal
fraction = $195,502.12/$389,550.22 = 0.5019 = 50.19%.

43. d. 14.93%

Amortization

N = 25 x 12

I = 8.5/12

PV = -125,000

FV = 0

PMT = $1,006.53

Do amortization:

Enter: 1 INPUT 60 AMORT

Int = $51,375.85

Prin = $9,015.95

Bal = $115,984.05

Total payments = 5 x 12 x $1,006.53

= $60,391.80.

% Repayment $9,015.95

44.
a. $7,757.16

Amortization

Given:
Loan Value =
$100,000 Repayment
Period = 12 months

Monthly
Payment = $9,456

N
= 12

PV
= -100,000

PMT
= 9,456

FV
= 0

Solve
for I/YR = 2.00% x 12 = 24.005.

To
find the amount of principal paid in the third month (or period), use the
calculator's amortization feature. Enter:

3
INPUT 3 (to indicate the starting
and ending period you're

concerned with)

AMORT
(to activate the amortization function)

Interest
= $1,698.84

Principal
= $7,757.16

Balance
= $77,181.86

45. b. $18,508.81

Amortization

46. e. 8.94%

Amortization

Enter information into the calculator to
use its amortization

feature:

N = 360

I/YR = 8.5/12 = 0.7083

PMT = 1,000

FV = 0

Solve for PV = -$130,053.64 = Original
value of mortgage.

Enter: 1 INPUT 36 ê AMORT

Int 1-36 = $32,782.14

Prin 1-36 = $3,217.86

Total payments 1-36 = $36,000.

Percentage of total payments ($3,217.86

47.
c. $167,790.15

Remaining
balance on mortgage

Solve
for the monthly payment as follows:

N
= 30 x 12 = 360

I
= 9/12 = 0.75

PV
= -175,000

FV
= 0

Solve
for PMT = $1,408.09/month.

Use
the calculator's amortization feature to find the remaining principal balance:

5
yrs = 5 x 12 = 60 payments.

1
INPUT 60 AMORT

Interest $77,275.55

Principal $ 7,209.85

Balance $167,790.15

48.
d. $145,920.12

Remaining
balance on mortgage

Solve
for the monthly payment as follows:

N
= 30 x 12 = 360

I
= 8/12 = 0.667

PV
= -150,000

FV
= 0

Solve
for PMT = $1,100.65/month.

Use
the calculator's amortization feature to find the remaining principal balance:

3
x 12 = 36 payments

1
INPUT 36 AMORT

Interest $ 35,543.52

Principal
$ 4,079.88

Balance $145,920.12

49.
d. $141,937

Remaining
balance on mortgage

Solve
for the monthly payment as follows:

N
= 12 x 15 = 180

I
= 8.5/12 = 0.7083

PV
= -160,000

FV
= 0

PMT
= $1,575.58.

Use
the calculator's amortization feature to find the remaining principal balance:

1
INPUT 36 AMORT

Interest $ 38,658.34

Principal
$ 18,062.54

Balance $141,937.46

50.
e. 9.0438%

Effective
annual rate

Given:
Loan Value = $12,000 Loan Term = 10 years (120 months)

Monthly
Payment = $150

N
= 120

PV
= -12,000

PMT
= 150

FV
= 0

Solve
for I/YR = 0.7241 x 12 = 8.6892%. However, this is a nominal rate. To find the
effective rate, enter the following:

NOM%
= 8.6892

P/YR
= 12

Solve
for EFF% = 9.0438%.