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5) Jay Coleman just graduated. He plans to work for five years and then leave for the Australian
"Outback" country. He figures that he can save $3,500 a year for the first three years and $5,000
a year for the next two years. These savings will start one year from now. In addition, his family
gave him a $2,500 graduation gift. If he puts the gift, and the future savings when they start, into
an account that pays 7.75% compounded annually, what will his financial "stake" be when he
leaves for Australia five years from now? Round off to the nearest $1.
A) $36,082
B) $24,725
C) $30,003
D) $27,178
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
6) You are thinking of buying a miniature golf course. It is expected to generate cash flows of
$40,000 per year in years one through four and $50,000 per year in years five through eight. If
the appropriate discount rate is 10%, what is the present value of these cash flows?
A) $285,288
B) $167,943
C) $235,048
D) $828,230
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
7) You have been depositing money at the end of each year into an account drawing 8% interest.
What is the balance in the account at the end of year four if you deposited the following
amounts?
4 $400
A) $1,622
B) $2,207
C) $2,384
D) $2,687
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
30
8) You want to travel to Europe to visit relatives when you graduate from college three years
from now. The trip is expected to cost a total of $10,000. Your parents have deposited $5,000 for
you in a CD paying 6% interest annually, maturing three years from now. Aunt Hilda has agreed
to finance the balance. If you are going to put Aunt Hilda's gift in an investment earning 10%
annually over the next three years, how much must she deposit now so you can visit your
relatives in three years?
A) $3,757
B) $3,039
C) $3,801
D) $3,345
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value
Principles: Principle 1: Money Has a Time Value
9) What is the present value of the following uneven stream of cash flows? Assume a 6%
discount rate and end-of-period payments. Round to the nearest whole dollar.
3 $5,000
A) $10,588
B) $11,461
C) $12,688
D) $13,591
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
10) As a part of your savings plan at work, you have been depositing $250 per quarter in a
savings account earning 8% interest compounded quarterly for the last 10 years. You will retire
in 15 years and want to increase your contribution each year from $1,000 to $2,000 per year, by
increasing your contribution every four months from $250 to $500. Additionally, you have just
inherited $10,000, which you plan to invest now to earn interest at 12% compounded annually
for the next 15 years. How much money will you have in savings when you retire 15 years from
now?
A) $126,862
B) $73,012
C) $161,307
D) $194,415
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
31
11) Ronald Slump purchased a real estate investment with the following end-of-year cash flows:
4 $950
What is the present value of these cash flows if the appropriate discount rate is 20%?
A) $178
B) $160
C) $133
D) $767
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
12) You have just won a magazine sweepstakes and have a choice of three alternatives. You can
10 years. If the appropriate discount rate is 12%, which option should you choose?
A) $100,000 now
B) $10,000 perpetuity
C) $50,000 now and $150,000 in 10 years
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
13) Your parents are planning to retire in Phoenix, AZ in 20 years. Currently, the typical house
that pleases your parents costs $200,000, but they expect inflation to increase the price of the
house at a rate of 4% over the next 20 years. In order to buy a house upon retirement, what must
they save each year in equal annual end-of-year deposits if they can earn 10% annually?
A) $21,910.00
B) $7,650.94
C) $10,000.00
D) $14,715.52
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
32
14) You intend to purchase your dream PC upon graduation in two years. It will have a cost of
$2,975, including all attachments and sales tax. You just received a $3,000 pre-graduation gift
from your rich uncle that you intend to deposit in a money market account that pays 6% interest,
compounded monthly. How much of your pre-graduation gift will you need to deposit in order to
have $2,975 available for the purchase of the PC upon graduation?
A) $1,275
B) $2,588
C) $2,975
D) $1,567
E) $2,639
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value
Principles: Principle 1: Money Has a Time Value
15) Assume that two investments have a three-year life and generate the cash flows shown
below. Which of the two would you prefer?
3 $5,000 $2,000
A) Investment A, since it has the most even cash flows
B) Investment B, since it gives you the largest cash flows in earlier years
C) Neither, since they both have equal lives
D) Both investments are equally attractive
E) None of the above
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
33
16) You have just purchased an investment that generates the cash flows that are shown below.
You are able to invest your money at 5.75%, compounded annually. How much is this investment
worth today?
5 $3,450
A) $7,758
B) $4,521
C) $10,260
D) $8,467
E) $6,583
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
17) To evaluate and compare investment proposals, we must adjust all cash flows to a common
date.
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
18) Consider an investment that has cash flows of $500 the first year and $400 for the next four
years. If your opportunity cost is 10%, how much is this investment worth to you?
454.50 + 1152.61 = $1,607.11
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
19) If your opportunity cost is 10%, how much are you willing to pay for an investment
promising $750 per year for the first four years and $450 for the next six years?
2377.50 + 1338.51 = $3,716.01
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
8%
Value in year 20 of annuity of $2,000 per year for years 21 through 30 = $2,000(6.710) =
$13,420
Present value of annuity of $2,000 per year for years 21 through 30 = $13,420(.215) = $2,885.30
Total present value = $6,710 + $2,885.30 = $9,595.30
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
35
22) You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year
12%, what do you estimate that you will have in this account at retirement?
12 I/yr or I
FV = $430,071
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value of annuity
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
24) Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you
will need to withdraw $5,000 per year from a retirement fund to supplement your social security
payments. You expect to live to the age of 85. How much money should you place in the
retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12%
interest per year from the fund?
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value complex income stream
Principles: Principle 1: Money Has a Time Value
36
25) An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If
the opportunity rate is 6%, what is the present value of this investment?
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
26) What is the value (price) of a bond that pays $400 semiannually for 10 years and returns
$10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
27) Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One bond is
being offered from Hershey's and will mature in 10 years and pays 12% per year, compounded
quarterly. The other alternative is a Mars bond that will mature in 20 years and that pays 12% per
10%?
Topic: 6.3 Complex Cash Flow Streams
Keywords: present value complex income stream
Principles: Principle 1: Money Has a Time Value
37
28) In order to send your oldest child to law school when the time comes, you want to
accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6%
compounded annually, how much would you have to deposit if:
a. you want to deposit an amount annually at the end of each year?
b. you want to deposit one large lump sum today?
Topic: 6.3 Complex Cash Flow Streams
Keywords: future value
Principles: Principle 1: Money Has a Time Value
38
