Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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PROBLEMS
115
CHAPTER
SUMMARY
In Chapter 2, we derived the equations to calculate the present, future, or annual
worth
of
specific cash flow series. In this chapter, we have shown that these equa-
tions apply to cash flow series different from those for which the basic relations
are derived. For example, when a uniform series does not begin
in
peliod I, we
still use the
PIA factor
to
find the "present worth"
of
the series, except the P
value is located one period ahead
of
the first A value, not at time
O.
For arithmetic
and geometric gradients, the
P value
is
two periods ahead
of
where the gradient
starts. With this information, it
is
possible to solve for any
symbol-P,
A,
or
F-
for any conceivable cash flow series.
We have experienced some
of
the power
of
spreadsheet functions in determining
P, F, and A values once the cash flow estimates are entered into spreadsheet cells.
PROBLEMS
Present Worth Calculations
3.
I Because unintended lane changes by dis-
tracted drivers are responsible for 43%
of
all highway fatalities, Ford Motor Co. and
Volvo launched a program to develop tech-
nologies to prevent accidents by sleepy
drivers. A device costing
$260 tracks lane
markings and sounds an alert during lane
changes.
If
these devices are included in
100,000 new cars per year beginning
3 years from now, what wou
ld
be the pre-
sent worth
of
their cost over a 10-year
period at an interest rate
of
10
% per year?
3.2
One plan to raise money for Texas schools
involves an
"enrichment tax" that could col-
lect $56 for every student
ina
certain school
district.
If
there are 50,000 students in the
district and the cash flow begins 2 years
from now, what
is
the present worth
of
the
enrichment plan over a 5-year planning
period at an interest rate
of
8% per year?
3.3 Amalgamated Iron and
Steel purchased a
new machine for ram cambering large
I-beams.
The
company expects to bend
80 beams at $2000 per beam in each
of
the first 3 years, after which the company
expects to bend
100 beams
per
year at
$2500 per beam through year 8.
If
the
company's
minimum attractive rate
of
re-
turn is 18% per year, what is the present
worth
of
the expected income?
3.4 Rubbermaid
Plastics plans to purchase a
rectilinear robot for pulling parts from an
injection molding machine. Because
of
the
robot's speed, the company expects pro-
duction costs to decrease
by
$100,000 per
year
in
each
of
the first 3 years and by
$200,000 per year in the next 2 years. What
is
the present worth
of
the cost savings
if the company uses an interest rate
of
15
% per year on such investments?
3.5 Toyco Watercraft has a contract with a
parts supplier that involves purchases
amounting to
$150,000
per
yea
r,
with the
first purchase to be made now, followed by
similar purchases over the next 5 years.
Determine the present worth
of
the con-
tract at an interest rate
of
10
% per year.
3.6 Calculate the present worth
in
year 0
of
the following series
of
disbursements.
Assume that
i = 10% per year.
116
CHAPTER 3
Combining Factors
Year
Disbursement,
$
o
1
2
3
4
5
o
3500
3500
3500
5000
5000
Year
Disbursement,
$
6
7
8
9
10
5000
5000
5000
5000
5000
Annual
Worth
Calculations
3.7
Cisco's
gross revenue (the percentage
of
revenue left after subtracting the
cost
of
goods so
ld
) was 70.1 %
of
total revenue
over
a certain
4-year
period.
If
the total
revenue was
$5.4
billion for the first 2 years
and $6.1 billion
for
the last 2 years,
what
was the
equivalent
annual worth
of
the
gross revenue
over
that
4-year
period at an
interest rate
of
20
%
per
year?
3.8
BKM
Systems
sales revenues are shown
below. Calculate the
equiva
l
ent
annual
worth (years
1 through 7), using an inter-
est rate
of
10% per year.
Year
Disbursement,
$
o
1
2
3
4000
4000
4000
Year
Disbursement,
$
4
5
6
7
5000
5000
5000
5000
3.9 A metallurgical
engineer
decides to
set
aside money
for
his newborn
daughter's
college education.
He
estimates that
her
needs will
be
$20,000
on her l7th, 18th,
19th, and
20th birthdays.
If
he plans to
make uniform deposits starting 3 years
from now and continue through
year
16,
what
shou
ld
be
the si
ze
of
each
deposit
,
if
the
account
earns interest at a rate
of
8%
per year?
3. 10 Calculate the
annua
l worth
in
years I
through
10
of
the following series
of
in-
comes
and expenses,
if
the interest rate is
1
0% per year.
Year
o
1-6
7-10
3.
11
3.12
3.13
3.14
3.15
Income,
$lYear
10,000
800
900
Expense,
$lYear
2000
200
300
How
much
money would you have to pay
each
year
in 8 equal
payments
, starting
2 years from today, to repay a
$20,000
loan received
from
a relative today, if the
interest rate is
8%
per year?
An industrial
engineer
is planning for
hi
s
early retirement 25 years from now.
He
believes
he
can comfortably set
aside
$10,000
each
year
starting now.
If
he plans
to start withdrawing money 1
year
after he
makes his last deposit (i.e.,
year
26),
what
uniform
amount
could
he withdraw
each
year
for
30
years,
if
the account earns in-
terest at a rate
of
8%
per
year?
A rural utility
company
provides standby
power
to
pumping
stations using diesel-
powered
generators.
An
alternative has
arisen
whereby
the utility
could
use nat-
ural gas to
power
the generators, but it will
be a few years before the gas
is
available
at
remote
sites.
The
utility estimates that
by switching to gas, it will save
$15,
000
per year, starting 2 years from now. At an
interest rate
of
8%
per
year,
determine
the
equivalent
annual worth (years I through
10)
of
the projected savings.
The
operating
cost
of
a pulverized coal cy-
clone
furnace is
expected
to
be
$80,000
per
year.
If
the
steam
produced
will
be
needed
only
for
5 years beginning
now
(i.e., years
o through 5),
what
is
the equivalent annual
worth in years
1 through 5
of
the operating
cost
at an interest rate
of
10% per year?
An entrepreneurial electrical
engineer
has
approacbed a large water utility with a pro-
posal that promises to reduce the utility's
power
bill
by
at
least
15
% per year
for
the next 5 years through installation
of
patented surge protectors. The proposal
states that the engineer will get
$5000 now
and annual payments that are equivalent to
75%
of
the power savings achieved from
the devices. Assuming the savings are the
same every year (i.e.,
15
%) and that the
utility's power bill is
$1
million per year,
what would be the equivalent uniform
amount (years
I through 5)
of
the pay-
ments to the engineer? Assume the utility
uses an interest rate
of
6% per year.
3.
16 A large water utility
is
planning to upgrade
its SCADA system for controlling well
pumps, booster pumps, and disinfection
equipment, so that everything can be con-
trolled from one site. The first phase will
reduce labor and travel costs by
$28,000
per year. The second phase will reduce
costs by an additional
$20,000 per year.
If
phase I savings occur in years 0,
1,2,
and
3 and phase II occurs
in
years 4 through
10, what is the equivalent annual worth
of
the upgraded system in years 1 through 10
at an interest rate
of
8% per year?
3.
17
A mechanical engineer who recently grad-
uated with a master's degree
is
contemplat-
ing starting his own commercial heating
and cooling company. He can purchase a
Web page design package aimed at deliver-
ing information only for
$600 per year.
If
his business is successful, he will purchase
a more elaborate e-commerce package cost-
ing
$4000 per year.
If
the engi neer purchases
the less expensive page now (beginning-
of-year payments) and he purchases the
e-commerce package 1 year from now (also
beginning-of-year payments), what is the
equivalent annual worth
of
costs for the
website for a 5-year period (years 1 through
5) at an interest rate
of
12 % per year?
Future
Worth Calculations
3
.1
8 Lifetime savings accounts, known as LSAs,
would allow people to invest after-tax
PROBLEMS
117
money without being taxed on any
of
the
gains.
If
an engineer invests $10,000 now
and
$10,000 each year for the next
20 years, how much will be in the account
immediately after the last deposit
if
the ac-
count grows by
15
% per year?
3.
19
How much money was deposited each
year for 5 years
if
the account is now
worth
$100,000 and the last deposit was
made 10 years ago? Assume the account
earned interest at 7% per year.
3.20 Calculate the future worth (in year 11)
of
the following income and expenses,
if
the
interest rate is 8% per year.
Year
o
1-6
7-
11
Income,
$
12,000
800
900
Expense,
$
3000
200
200
Random
Placement
and
Uniform Series
3.21 What is the equivalent worth
in
year 5
of
the following series
of
income and dis-
bursements,
if
the interest rate
is
] 2% per
year?
Year
Income,
$
Expense,
$
0 0
9000
1-5
6000 6000
6-8
6000
3000
9-14
8000
5000
3.22 Use the cash flow diagram below to calcu-
late the amount
of
money in year 5 that
is
equivalent to all the cash flows shown,
if
the interest rate is 12% per year.
o 1
234
6 7 8 9
10
II
12
13
Year
$1000
$2000
118
CHAPTER 3 Combining Factors
3.23
3.24
3.25
By spending $10,000 now and $25,000
three years from now, a plating company
can increase its income
in
years 4 through
10. At an interest rate
of
12% per year,
how much extra income per year would be
needed
in
years 4 through 10 to recover
th
e investment?
Si
erra Electric Company is considering the
purchase
of
a hillside ranch for possible use
as
a windmill farm sometime in the future.
The owner
of
the 500-acre ranch will sell for
$3000 per acre
if
the company will pay
herin
two payments
-one
payment now and an-
other that is twice as large 3 years from now.
If
the transaction interest rate
is
8% per year,
what
is
the amount
of
the first payment?
Two equal deposits made
20 and
21
years
ago, respectively, will allow a retiree to
withdraw $
J 0,000 now and $10,000 per
year for
14
more years.
If
the account
earned interest at
10%
per year, how large
was each deposit?
3.26 A concrete and building materials com-
pany is trying to bring the company-
funded portion
of
its employee retirement
fund into compliance with
HB-301.
The
company has already deposited $20,000
in
each
of
the last 5 years. How much must
be deposited now
in
order for the fund to
have
$350,000 three years from now,
if
the
fund grows at a rate
of
15
% per year?
3.27 Find
th
e value
of
x below such that the
pos
iti
ve cash flows will be exactly equiva-
lent to
th
e negative cash flows,
if
the inter-
est rate
is
J 4% per year.
$7
00
$
700
x
+
0
1 2
3
4 5
6 7 8 9
10
11
12 Year
$8
00
$8
00
$
950
3.28
o
3.29
o
3.30
In attempting to obtain a swing loan from a
local bank, a general contractor was asked
to provide an estimate
of
annual expenses.
One component
of
the expenses is shown
in the cash flow diagram below. Convert
the amounts shown into an equivalent uni-
form annual amount
in
years 1 through 8,
using
an
interest rate
of
12% per year.
2 3 4 5 6 7 8 Year
t t
$
1000
$3
000
$
5000
Determine the value
in
year 8 that is
equivalent to the cash flows below.
Use an
interest rate
of
12% per year.
2 3 4 5 6 7 8 Year
$1500
$
2500
$
2500
Find the value
of
x
in
the diagram below
that will make the equivalent present
worth
of
the cash flow equal to $15,000,
if
the interest rate is 15%
per
year.
P = $
15
,
000
o
2 3 4 5 6 7 Year
$
1000
$2000
x
3.31 Calculate the amount
of
money in year 3
that is equivalent to the following cash
flows,
if
the interest rate is
16
%
per
year.
a
I
2
3
3.33
Year
a
2
3
4
5
5000
3500
3500
3500
4
5
6
7
5000
5000
5000
5000
Calculate the value
of
x for the cash flows
below such that the equivalent total value
in
year 8 is $20,000, using an interest rate
of
15
% per year.
Cash
Flow, $ Year
Cash
Flow, $
2000 6 x
2000
7
x
x
8
x
x
9
1000
x
10
1000
x
11
1000
Shifted Arithmetic
Gradients
3.34
San Antonio
is
considering various op-
tions for providing water
in
its 50-year
plan, including desalting.
One brackish
aquifer
is
expected to yield desalted water
that will generate revenue
of
$4.1 million
per year for the first 4 years, after which
less production will decrease revenue each
year
by
$50,000 per year.
If
the aquifer
will be totally depleted in 25 years,
whatis
the present worth
of
the desalting option at
an interest rate
of
6%
per
year? .
3.35 Exxon-Mobil
is
planning to sell a number
of
producing oil wells.
The
wells are ex-
pected to produce
100,000 barrels
of
oil
3.37
3.38
Year
a
2
3
PROBLEMS
119
per
year for 8 more years at a selling price
of
$28 per barrel for the next 2 years, in-
creasing by
$1
per ban·el through year
8.
How much should
an
independent refiner
be willing to pay for the wells now, if the
interest rate
is
12% per year?
Burlington Northern
is
considering the
elimination
of
a railroad grade crossing by
constructing a dual-track overpass.
The
railroad subcontracts for maintenance
of
its crossing gates at $11,500 per year. Be-
ginning 4 years from now, however, the
costs are expected to increase by
$LOOO
per year into the foreseeable future (that
is,
$12,500 4 years from now, $13,500 five
years from now, etc.). The overpass will
cost $1.4 million (now) to build, but it will
eliminate
100%
of
the auto-train collisions
that have cost an average
of
$250,000 per
year.
If
the railroad uses a lO-year study
period and an interest rate
of
10%
per
year,
determine whether the railroad should
build the overpass.
Levi Strauss
has
some
of
its
jeans
stone-
washed under a contract with independent
U.S. Garment Corp.
If
U.S. Garment's op-
erating cost per machine is
$22,000 per
year for years 1 and 2 and then it increases
by
$1000 per year through year 5, what
is
the equivalent uniform annual cost per
machine (years 1 through 5) at an interest
rate
of
12% per year?
Herman Trucking Company's receipts and
disbursements (in
$1000) are shown
below. Calculate the future worth
in
year 7
at an interest rate
of
10% per year.
Cash
Flow, $ Year
Cash
Flow, $
-
10
,000
4,000
3,000
4,000
4
5
6
7
5,000
- 1,000
7,000
8,000
3.39 Peyton Packing has a ham cooker that has
the cost stream below.
If
the interest rate
is
120
CHAPTER
3
Combining
Factors
3.40
3.41
Year
0
1
2
3
4
15
% per year, determine the annual worth
(in years 1 through 7)
of
the costs.
Year
o
2
3
Cost,
$
4,000
4,000
3,000
2,000
Year
4
5
6
7
Cost,
$
6,000
8,000
10
,000
12
,000
A start-up company selling color-keyed
carnuba car wax borrows
$40,000 at
an
interest rate
of
10% per year and wishes
to
repay the loan over a 5-year period
with annual payments such that the third
through fifth payments are
$2000 greater
than the first two. Determine the size
of
the first two payments.
For the cash flows below, find the value
of
x that makes the present worth
in
year 0
equal to $11,000 at an interest rate
of
12%
per year.
Cash Flow, $ Year Cash Flow, $
200 5 700
300
6
8
00
400 7 900
x 8 1000
600
9
1100
Shifted Geometric Gradients
3.42 In an effort to compensate for shrinking
land-line customers, SBC and Bell South
(owners
of
Cingular Wireless LLC) got
into a bidding war with Vodaphone to
acquire AT&T Wireless.
The
initial
$11
per share offer escalated to $13 for the
2.73 billion shares
of
AT&T Wireless.
If
the buyout took exactly 1 year to close (i.e.,
end
of
year 1), what would be the present
worth today (time
0)
of
the acquisition for
profits
of
$5.3 billion in year 2, increasing
by 9% per year through year
II?
Assume
SBC and Bell South use a rate
of
return
of
15
% per year.
3.43 A successful alumnus
is
planning to make
a contribution to the community college
from whjch he graduated.
The
donation is
to be made over a 5-year period beginning
now, a total
of
six payments. It will sup-
port five preengineering students per year
for
20 years, with the first scholarship
to be awarded immediately (a total
of
21
scholarships). The cost
of
tuition at the
school
is
$4000 per year and
is
expected
to stay at that amount for 3 more years.
After that time (i.e., year 4), the tuition
is
expected to increase by 8% per year.
If
the
college can invest the money and earn in-
terest at a rate
of
10% per year, what size
must the donations be?
3.44 Calculate the present worth (year
0)
of
a
lease that requires a payment
of
$20,000
now and amounts increasing by 5% per
year through year
10. Use an interest rate
of
14% per year.
3.45 Calculate the present worth for a machine
that has an initial cost
of
$29,000, a life
of
10 years, and an annual operating cost
of
$13,000 for the first 4 years, increasing by
10% per year thereafter.
Use an interest
rate
of
lO%
per year.
3.46
A-I
Box Company
is
planning to lease a
computer system that will cost (with ser-
vice)
$15,000 in year
1,
$16,500
in
year 2,
and amounts increasing by
10% each year
thereafter. Assume the lease payments
must be made
at
the beginning
of
the ye
ar
and that a 5-year lease is planned. What
is
the present worth (year 0) if the company
uses a mjnimum attractive rate
of
return
of
16% per year?
3.47 Dakota Hi-C Steel signed a contract that
will generate revenue
of
$210,000 now,
$222,600 in year 1, and amounts increas-
ing·by 8% per year through year 5. Calcu-
late the future worth
of
the contract at an
interest rate
of
8% per year.
Shifted Decreasing
Gradients
3.48 Find the present worth (at time 0)
of
the
chrome plating costs in the cash flow dia-
gram. Assume
i = 12% per year.
p=?
o
$2000
1800
2 3 4 5
t
J?OO
1000
1600
1400
-
Year
3.49 Compute the present worth (year 0)
of
the
following cash flows at
i = 12% per year.
Year
Amount,
$ Ye
ar
Amount,
$
0
5000
8
700
1-5
1000
9
600
6
900
10
500
7
800
II
400
3.50 For the cash flow tabulation, calculate the
equivalent uniform annual worth
in
peri-
ods I through 10, if the interest rate
is
10%
per year.
Year
Amount,
$ Year
o
2
3
4
5
2000
2000
2000
2000
2000
2500
FE
REVIEW PROBLEMS
6
7
8
9
10
Amount,
$
2400
2300
2200
2100
2000
3.
54 The annual worth
in
years 4 through 8
of
an
amount
of
money x that will be received
2 years from now
is
$4000. At
an
interestrate
of
10
% per year, the value
of
x
is
closest to
(a) Less than $12,000
(b) $12,531
(c) $12,885
(d)
More than $13,000
FE REVIEW PROBLEMS
12
1
3.51 Prudential Realty has an escrow account
for one
of
its property management clients
that
cunently
contains $20,000. How long
will it take to deplete the account if the
client withdraws
$5000 now, $4500 one
year from now, and amounts decreasing
by
$500 each year thereafter,
if
the account
earns interest at a rate
of
8% per year?
3
.5
2
The
cost
of
spacers used around fuel rods
in
liquid-metal fast breeder reactors has been
decreasing because
of
the availability
of
im-
proved temperature-resistant ceramic mate-
rials. Determine the present worth (in year
0)
of
the costs shown in the diagram below,
using an interest rate
of
15% per year.
o
$2000
1800
2 3 4 5
t
1200 1000
1600 1400
Year
3.53 Compute the future worth
in
year 10 at i =
10% per year for the cash flow shown below.
0
F=?
2 3 4 5 6 7 8 9
10
Year
4200
4000
4600
4400
$5000
4800
3.55
The
multistate Powerball Lottery, worth
$182 million, was won by a single indi-
vidual who had purchased five tickets at
$1
each. The individual was given two
choices: Receive 26 payments
of
$7 mil-
lion each, with the first payment to be
made now and the rest to be made at the
end
of
each
of
the next 25 years;
or
receive
122
CHAPTER
3 Combining Factors
a single lump-sum payment
now
that
would be equivalent to the 26 payments
of
$7 million each.
If
the state uses an inter-
est rate
of
4% per year, the amount
of
the
lump-sum payment is closest to
(a) Less than $109 million
(b)
$109,355,000
(c) $116,355,000
(d)
Over $117 million
3.56 The attendance at the annual El Paso Live-
stock Show and Rodeo has been declining
for the past 5 years. The attendance was
25,880
in
2000 and
13
,500
in
2004 (a
15
%
per year decrease).
If
the average ticket
price was $10 per person over that time
period, the present worth
of
the income
in
year 1999 (i.e., year 1999
is
time 0) for the
years 2000 through 2004 at
an
interest rate
of
8% per year is represented by which
of
the following equations?
(a) P = 250,880{1 - [(1 + 0.15)5/(1 +
0.08)5
])
/(0.08
- 0.15) = $1,322,123
(b) P = 250,880{ 1 -
[(1
- 0.15)4/(1 +
0.08)4]} / (0.08 + 0.] 5) = $672,260
(c) P = 250,880{1 -
[(1
+
0.15t/(l
+
0.08)4]}/(0.08 - 0.15) = $1,023,489
(d)
P = 250,880{1 -
[(1
- 0.15)5/(1 +
0.08)5
])
/ (0.08 + 0.15) = $761,390
3.57 A company that manufactures hydrogen
sulfide monitors
is
planning to make de-
posits sllch that each one
is
5% larger
than the preceding one. How large must
the first deposit be (at the end
of
year
1)
if the deposits extend through year
10
and the fourth deposit
is
$1250? Use an
interest rate
of
10
% per year.
(a)
$1312
.
50
(b) $1190.48
(c) $1133.79
(d) $1079.80
3.58
If
$10,000
is
borrowed now at 10% per
year interest, the balance at the end
of
year 2 after payments
of
$3000
in
year 1
and $3000
in
year 2 will be closest to
(a) Less than $5000
(b) $5800
(c) $6100
(d)
More than $7000
3.59 The annual deposit needed in years 1
through 5 to provide for
an
annual with-
drawal
of
$1000 for 20 years beginning
6 years from now at an interest rate
of
10%
per year is closest to
(a)
$1395
(b)
$1457
(c)
$1685
(d)
More than $1700
3.60 The maintenance cost for a certain ma-
chine
is
$1000 per year for the first 5 years
and $2000 per year for the next 5 years. At
an interest rate
of
10% per year, the annual
worth in years 1 through 10
of
the mainte-
nance cost is closest to
(a)
$1255
(b) $1302
(c)
$1383
(d)
$1426
3.
61
If
a company wants to have $100,000
in
a
contingency fund
10
years from now, the
amount the company must deposit each
year in years 6 through 9, at
an
interest
rate
of
10% per year, is closest to
(a)
$19
,
588
(b)
$20
,
614
(c) $21,547
Cd)
$22,389
3.62
If
a person begins saving money by de-
positing $1000 now and then increases the
deposit by $500 each year through year
10, the amount that will be
in
the account
in
year 10 at
an
interest rate
of
] 0% per
year is closest to
(a) $21,662
(b)
$35
,
687
(c) $43,872
(d) $56,186
3.
63
If
a sum
of
$5000
is
deposited now, $7000
two years from now, and $2000 per year in
years 6 through
10,
the amount in year 10
at an interest rate
of
lO
% per year will be
closest to
E
XTENDED
EXERCISE
EXTENDED EXERCISE
(a) Less than $40,000
(b) $40,
185
(c) $42,200
(d)
$43,565
PRESERVING LAND FOR PUBLIC USE
123
The
Trust for Public Land is a national organization that purchases and oversees the
improvement
of
large land sites for government agencies at all levels. Its mission
is
to ensure the preservation
of
the natural resources, while providing necessary,
but minimal, development for recreational use
by
the public. All Trust projects are
evaluated at 7% per year, and Trust reserve funds earn 7% per year.
A southern
U.S. state, which has long-term groundwater problems, has asked
the Trust to manage the purchase
of
10,000 acres
of
aquifer recharge land and the
development
of
three parks
of
different use types on the land.
The
10,000 acres
will be acquired
in
increments over the next 5 years with $4 million expended im-
mediately on purchases. Total annual purchase amounts are expected to decrease
25% each year through the fifth year and then cease for this particular project.
A city with
1.5
million citizens immediately to the southeast
of
this acreage
relies heavily on the aquifer's water. Its citizens passed a bond issue last year,
and the city government now has available $3 million for the purchase
of
land.
The
bond interest rate is an effective
7%
per
year.
The
civil engineers working on the park plan intend to complete all the devel-
opment over a 3-year period starting in year 4, when the amount budgeted
is
$550,000. Increases
in
construction costs are expected to be $100,000 each year
through year
6.
At a recent meeting, the following agreements were made:
• Purchase the initial land increment now. Use the bond issue funds to assist
with this purchase. Take the remaining amount from Trust reserves.
• Raise the remaining project funds over the next 2 years in equal annual amounts.
• Evaluate a financing alternative (suggested informally by one individual at
the meeting)
in
which the Trust provides all funds, except the $3 million
available now, until the parks development is initiated
in
year 4.
Questions
Use hand or computer computations to find the following.
I. For each
of
the 2 years, what
is
the equivalent annual amount necessary to
supply the remaining project funds?
2.
If
the Trust did agree to fund all costs except the $3 million bond proceeds now
available, determine the equivalent annual amount that must be raised
in
years
4 through 6
to
supply all remaining project funds. Assume the Trust w
ill
not
charge any extra interestoverthe 7% to the state or city on the borrowed funds.
4
w
u
Nominal and Effective
I nterest Rates
In all
engineering
economy
relations
developed
thus far,
the
interest rate h
as
been
a constant, annual value. For a substantial
percentage
of
th
e
proj
ec
ts
evaluated
by
professional
engineers
in
practice,
the
interest rate
is
co
m-
pounded
more
frequently
than
once
a year;
frequencies
such
as
semiannual,
quarterly,
and
monthly
are
common.
In
fact, weekly,
daily
, and even
continu
-
ous
compounding
may
be
experienced
in
some
project
evaluations. Also, in
our
own
personal lives,
many
of
the
financial
considerations
we
make-loan
s
of
all
types
(home
mortgages,
credit
cards,
automobiles,
boats), check
ing
and savings accounts, investments, stock
option
plans,
etc
.
-have
inter
est
rates
compounded
for
a ti
me
period
shorter
than 1 year. This requires
the
in-
troduction
of
two
new
terms-nominal
and
effective
interest
rate
s.
This
chapter
explains
how
to
understand
and
use
nominal
and effective
interest
rates in
engineering
practice
and
in
daily
life situations. The
flow-
c
hart
on
calculating an
effective
interest
rate in
the
appendi
x
to
thi
s c
hapter
serves
as
a reference
throughout
the
sections
on
nominal
and
effec
tive
rate
s,
as well
as
continuous
compounding
of
interest
. This
chapter
also
develops
equivalence
calculations
for
any
compounding
frequency
in
combination
with
any cash
flow
frequency
.
The case
study
includes
an
evaluation
of
several
financing
plans
for
the
purchase
of
a house.