Basics of Engineering Economy

Leland Blank, Anthony Tarquin

Chapter 2 Factors How Time and Interest Affect Money - all with Video Answers

Educators

Chapter Questions

Problem 1

Find the correct numerical value for the following factors from the compound interest factor tables.
a. $(F / P, 10 \%, 20)$
b. $(A / F, 4 \%, 8)$
c. $(P / A, 8 \%, 20)$
d. $(A / P, 20 \%, 28)$
e. $(F / A, 30 \%, 15)$

Check back soon!

Problem 2

Beckton Steel Products, a company that specializes in crankshaft hardening, is investigating whether it should update certain equipment now or wait and do it later. If the cost now is $$\$ 180,000$$, what would the equivalent amount be 3 years from now at an interest rate of $10 \%$ per year?

Check back soon!

Problem 3

By filling carbon nanotubes with miniscule wires made of iron and iron carbide, incredibly thin nano wires could be extruded by blasting the carbon nanotubes with an electron beam. If Gentech Technologies spends $$\$ 2.7$$ million now in developing the process, how much would the company have to receive in licensing fees 3 years from now to recover its investment at 20\% per year interest?

Check back soon!

Problem 4

Arctic and Antarctic regions are harsh environments in which to take data. A TempXZ 3000 portable temperature recorder can take and store 32,767 measurements at $-40^{\circ} \mathrm{C}$ to $150^{\circ} \mathrm{C}$. A research team from the University of Nova Scotia needs 20 of the recorders, and they are trying to decide whether they should buy them now at $$\$ 649$$ each or purchase them 2 years from now, which is when they will be deployed. At an interest rate of $8 \%$ per year, how much will the 20 recorders have to cost in 2 years to render their decision indifferent?

Check back soon!

Problem 5

Since many U.S. Navy aircraft are at or near their usual retirement age of 30 years, military officials want a precise system to assess when aircraft should be taken out of service. A computational method developed at Carnegie Mellon University maps in 3-D the microstructure of aircraft materials in their present state so that engineers can test them under different conditions of moisture, salt, dirt, etc. Military officials can then determine if an aircraft is fine, is in need of overhaul, or should be retired. If the 3-D system allows the Navy to use one airplane 2 years longer than it normally would have been used, thereby delaying the purchase of a $$\$ 20$$ million aircraft for 2 years, what is the present worth of the assessment system at an interest rate of $15 \%$ per year?

Check back soon!

Problem 6

GE Marine Systems is planning to supply a Japanese shipbuilder with aero-derivative gas turbines to power 11 DD-class destroyers for the Japanese Self-Defense Force. The buyer can pay the total contract price of $$\$ 2,100,000$$ two years from now (when the turbines will be needed) or an equivalent amount now. At an interest rate of $15 \%$ per year, what is the equivalent amount now?

Check back soon!

Problem 7

A maker of microelectromechanical systems can reduce product recalls by $10 \%$ if it purchases new packaging equipment. If the cost of the new equipment is expected to be $$\$ 40,000$$ four years from now, how much could the company afford to spend now (instead of 4 years from now) if it uses a minimum attractive rate of return of $12 \%$ per year?

Check back soon!

Problem 8

How much money could Tesla-Sino Inc., a maker of superconducting magnetic energy storage systems, afford to spend now on new equipment in lieu of spending $$\$ 85,000$$ five years from now, if the company's rate of return is $18 \%$ per year?

Check back soon!

Problem 9

French car maker Renault signed a $$\$ 95$$ million contract with ABB of Zurich, Switzerland, for automated underbody assembly lines, body assembly workshops, and line control systems. If ABB will be paid in 3 years (when the systems are ready), what is the present worth of the contract at $12 \%$ per year interest?

Check back soon!

02:40

Problem 10

What is the future worth 6 years from now of a present cost of $$\$ 175,000$$ to Corning, Inc. at an interest rate of $10 \%$ per year?

Narayan Hari

Numerade Educator

Problem 11

A pulp and paper company is planning to set aside $$\$ 150,000$$ now for possibly replacing its large synchronous refiner motors. If the replacement isn't needed for 8 years, how much will the company have in the account if it earns interest at a rate of $8 \%$ per year?

Check back soon!

Problem 12

A mechanical consulting company is examining its cash flow requirements for the next 7 years. The company expects to replace office machines and computer equipment at various times over the 7-year planning period. Specifically, the company expects to spend $$\$ 7000$$ two years from now, $$\$ 9000$$ three years from now, and $$\$ 5000$$ five years from now. What is the present worth of the planned expenditures at an interest rate of $10 \%$ per year?

Check back soon!

00:51

Problem 13

A proximity sensor attached to the tip of an endoscope could reduce risks during eye surgery by alerting surgeons to the location of critical retinal tissue. If a certain eye surgeon expects that by using this technology, he will avoid lawsuits of $$\$ 0.6$$ and $$\$ 1.35$$ million 2 and 5 years from now, respectively, how much could he afford to spend now if his out-of-pocket costs for the lawsuits would be only $10 \%$ of the total amount of each suit? Use an interest rate of $10 \%$ per year.

Niamat Khuda

Numerade Educator

Problem 14

Irvin Aerospace of Santa Ana, CA, was awarded a 5-year contract to develop an advanced space capsule airbag landing attenuation system for NASA's Langley Research Center. The company's computer system uses fluid structure interaction modeling to test and analyze each airbag design concept. What is the present worth of the contract at $10 \%$ per year interest if the annual cost (years 1 through 5) is $$\$ 8$$ million per year?

Check back soon!

Problem 15

Julong Petro Materials Inc. ordered $$\$ 10$$ million worth of seamless tubes for its drill collars from the Timken Company of Canton, Ohio. (A drill collar is the heavy tubular connection between a drill pipe and drill bit.) At $10 \%$ per year interest, what is the annual worth of the purchase over a 10-year amortization period?

Check back soon!

Problem 16

Improvised explosive devices (IEDs) are responsible for many deaths in times of war. Unmanned ground vehicles (robots) can be used to disarm the IEDs and perform other tasks as well. If the robots cost $$\$ 140,000$$ each and the U.S. Army signs a contract to purchase 4000 of them now, what is the equivalent annual cost of the contract if it is amortized over a 3-year period at $8 \%$ per year interest?

Check back soon!

Problem 17

The U.S. Navy's robotics lab at Point Loma Naval Base in San Diego is developing robots that will follow a soldier's command or operate autonomously. If one robot would prevent injury to soldiers or loss of equipment valued at $$\$ 1.5$$ million, how much could the military afford to spend on the robot and still recover its investment in 4 years at $8 \%$ per year?

Check back soon!

00:53

Problem 18

PCM Thermal Products uses austenitic nickelchromium alloys to manufacture resistance heating wire. The company is considering a new annealing-drawing process to reduce costs. If the new process will cost $$\$ 2.55$$ million dollars now, how much must be saved each year to recover the investment in 6 years at an interest rate of $14 \%$ per year?

Xiaomeng Zhang

Numerade Educator

Problem 19

A green algae, chlamydomonas reinhardtii, can produce hydrogen when temporarily deprived of sulfur for up to 2 days at a time. How much could a small company afford to spend now to commercialize the process if the net value of the hydrogen produced is $$\$ 280,000$$ per year? Assume the company wants to earn a rate of return of $18 \%$ per year and recover its investment in 8 years.

Check back soon!

View

Problem 20

HydroKlean, LLC, an environmental soil cleaning company, borrowed $$\$ 3.5$$ million to finance startup costs for a site reclamation project. How much must the company receive each year in revenue to earn a rate of return of $20 \%$ per year for the 5 -year project period?

Rashmi Sinha

Numerade Educator

Problem 21

A VMB pressure regulator allows gas suppliers and panel builders to provide compact gas handling equipment, thereby minimizing the space required in clean rooms. Veritech Micro Systems is planning to expand its clean room to accommodate a new product design team. The company estimates that it can reduce the space in the clean room by 7 square meters if it uses the compact equipment. If the cost of construction for a clean room is $$\$ 5000$$ per square meter, what is the annual worth of the savings at $10 \%$ per year interest if the cost is amortized over 10 years?

Check back soon!

Problem 22

New actuator element technology enables engineers to simulate complex computer-controlled movements in any direction. If the technology results in cost savings in the design of new roller coasters, determine the future worth in year 5 of savings of $$\$ 70,000$$ now and $$\$ 90,000$$ two years from now at an interest rate of $10 \%$ per year.

Check back soon!

01:33

Problem 23

Under an agreement with the Internet Service Providers (ISPs) Association, ATT Communications reduced the price it charges ISPs to resell its high-speed digital subscriber line (DSL) service from $$\$ 458$$ to $$\$ 360$$ per year per customer line. A particular ISP, which has 20,000 customers, plans to pass $90 \%$ of the savings along to its customers. What is the total future worth of these savings in year 5 at an interest rate of $10 \%$ per year?

Charlene Bische

Numerade Educator

Problem 24

Southwestern Moving and Storage wants to have enough money to purchase a new tractor-trailer in 5 years at a cost of $$\$ 290,000$$. If the company sets aside $$\$ 100,000$$ in year 2 and $$\$ 75,000$$ in year 3, how much will the company have to set aside in year 4 in order to have the money it needs if the money set aside earns $9 \%$ per year?

Check back soon!

Problem 25

Vision Technologies, Inc., is a small company that uses ultra-wideband technology to develop devices that can detect objects (including people) inside buildings, behind walls, or below ground. The company expects to spend $$\$ 100,000$$ per year for labor and $$\$ 125,000$$ per year for supplies for three years before a product can be marketed. At an interest rate of $15 \%$ per year, what is the total equivalent present worth of the company's expenses?

Check back soon!

01:01

Problem 26

How many years would it take for money to increase to four times the initial amount at an interest rate of $12 \%$ per year?

Amy Jiang

Numerade Educator

01:19

Problem 27

Acceleron, Inc., is planning to expand to new facilities in Indianapolis. The company will make the move when its real estate sinking fund has a total value of $$\$ 1.2$$ million. If the fund currently has $$\$ 400,000$$ and the company adds $$\$ 50,000$$ per year, how many years will it take for the account to reach the desired value, if it earns interest at a rate of $10 \%$ per year?

Kratika Bhadauria

Numerade Educator

Problem 28

The defined benefits pension fund of G-Tech Electronics has a net value of $$\$ 2$$ billion. The company is switching to a defined contribution pension plan, but it guaranteed the current retirees that they will continue to receive their benefits as promised. If the withdrawal rate from the fund is $$\$ 158$$ million per year starting 1 year from now, how many years will it take to completely deplete the fund if the conservatively managed fund grows at a rate of $7 \%$ per year?

Check back soon!

Problem 29

Allen Bradley claims that its XM1Z1A and XM442 electronic overspeed detection relay modules provide customers a cost-effective monitoring and control system for turbo machinery. If the equipment provides more efficient turbine performance to the extent of $$\$ 20,000$$ in year $$1, \$ 22,000$$ in year 2, and amounts increasing by $$\$ 2000$$ per year, how much could Mountain Power and Light afford to spend now at $10 \%$ per year interest if it wanted to recover its investment in 5 years?

Check back soon!

Problem 30

A low-cost noncontact temperature measuring tool may be able to identify railroad car wheels that are in need of repair long before a costly structural failure occurs. If the BNSF railroad saves $$\$ 100,000$$ in year $$1, \$ 110,000$$ in year 2 , and amounts increasing by $$\$ 10,000$$ each year for five years, what is the equivalent annual worth of the savings at an interest rate of $10 \%$ per year?

Check back soon!

02:00

Problem 31

Southwest Airlines hedged the cost of jet fuel by purchasing options that allowed the airline to purchase fuel at a fixed price for 5 years. If the market price of fuel was $$\$ 0.50$$ per gallon higher than the option price in year 1, $$\$ 0.60$$ per gallon higher in year 2 , and amounts increasing by $$\$ 0.10$$ per gallon higher through year 5 , what was the present worth of SWA's savings per gallon if the interest rate was $10 \%$ per year?

Lucas Finney

Numerade Educator

01:31

Problem 32

NMTeX Oil company owns several gas wells in Carlsbad, NM. Income from the depleting wells has been decreasing according to an arithmetic gradient for the past five years. If the income in year 1 from well no. 24 was $$\$ 390,000$$ and it decreased by $$\$ 15,000$$ each year thereafter, (a) what was the income in year 3 , and $(b)$ what was the equivalent annual worth of the income through year 5 at an interest rate of $10 \%$ per year?

Tanishq Gupta

Numerade Educator

Problem 33

The present worth of income from an investment that follows an arithmetic gradient was projected to be $$\$ 475,000$$. If the income in year one is expected to be $$\$ 25.000$$, how much would the gradient have to be in each year through year 8 if the interest rate is $10 \%$ per year?

Check back soon!

Problem 34

Very light jets (VLJs) are one-pilot, two-engine jets that weigh 10,000 pounds or less and have only five or six passenger seats. Since they cost half as much as the most inexpensive business jets, they are considered to be the wave of the future. MidAm Charter purchased 5 planes so that it can initiate service to small cities that have airports with short runways. MidAm expects revenue of $$\$ 1$$ million in year $$1, \$ 1.2$$ million in year 2 , and amounts increasing by $$\$ 200,000$$ per year thereafter. If the company's MARR is $10 \%$ per year, what is the future worth of the revenue through the end of year 5?

Check back soon!

01:43

Problem 35

Fomguard LLC of South Korea developed a hightech fiber-optic fencing mesh (FOM) that contains embedded sensors that can differentiate between human and animal contact. In an effort to curtail illegal entry into the United States, a FOM fence has been proposed for certain portions of the U.S. border with Canada. The cost for erecting the fence in year 1 is expected to be $$\$ 7$$ million, decreasing by $$\$ 500,000$$ each year through year 5. At an interest rate of $10 \%$ per year, what is the equivalent uniform annual cost of the fence in years 1 to 5 ?

Lucas Finney

Numerade Educator

Problem 36

For the cash flows shown, determine the future worth in year 5 at an interest rate of $10 \%$ per year.
$$
\begin{array}{lccccc}
\text { Year } & 1 & 2 & 3 & 4 & 5 \\
\hline \text { Cash Flow } & \$ 300,000 & \$ 275,000 & \$ 250,000 & \$ 225,000 & \$ 200,000
\end{array}
$$

Check back soon!

Problem 37

Verizon Communications said it plans to spend $$\$ 22.9$$ billion in expanding its fiber-optic Internet and television network through 2010 so that it can compete with cable TV providers like Comcast Corp. If the company gets 950,000 customers in year 1 and grows its customer base by $20 \%$ per year, what is the present worth of the subscription income through year 5 if income averages $$\$ 600$$ per customer per year and the company uses a MARR of $10 \%$ per year?

Check back soon!

Problem 38

A concept car that will get 100 miles per gallon and carry 4 persons would have a carbon-fiber and aluminum composite frame with a 900 cc threecylinder turbodiesel/electric hybrid power plant. The extra cost of these technologies is estimated to be $$\$ 11,000$$. If gasoline savings over a comparable conventional car would be $$\$ 900$$ in year 1 , increasing by $10 \%$ each year, what is the present worth of the savings over a 10-year period at an interest rate of $8 \%$ per year?

Check back soon!

01:34

Problem 39

The National Institute on Drug Abuse has spent $$\$ 15$$ million on clinical trials toward finding out whether two vaccines can end the bad habits of nicotine and cocaine addiction. A Switzerlandbased company is now testing an obesity vaccine. If the vaccines are semi-successful such that treatment costs and medical bills are reduced by an average of $$\$ 15,000$$ per person per year, what is the present worth of the vaccines if there are 10 million beneficiaries in year 1 and an additional $15 \%$ each year through year 5? Use an interest rate of $8 \%$ per year.

Narayan Hari

Numerade Educator

02:30

Problem 40

Find the future worth in year 10 of an investment that starts at $$\$ 8000$$ in year 1 and increases by $10 \%$ each year. The interest rate is $10 \%$ per year.

Jonathan Tapiwa

Numerade Educator

Problem 41

The effort required to maintain a scanning electron microscope is known to increase by a fixed percentage each year. A high-tech equipment maintenance company has offered its services for a fee that includes automatic increases of $7 \%$ per year after year 1. A certain biotech company offered $$\$ 75,000$$ as prepayment for a 3 year contract to take advantage of a temporary tax loophole. If the company used an interest rate of $12 \%$ per year in determining how much it should offer, what was the service fee amount that it assumed for year 1 ?

Check back soon!

03:06

Problem 42

Hughes Cable Systems plans to offer its employees a salary enhancement package that has revenue sharing as its main component. Specifically, the company will set aside $1 \%$ of total sales for yearend bonuses for all its employees. The sales are expected to be $$\$ 5$$ million the first year, $$\$ 5.5$$ million the second year, and amounts increasing by $10 \%$ each year for the next 5 years. At an interest rate of $8 \%$ per year, what is the equivalent annual worth in years 1 through 5 of the bonus package?

Joanna Ramsey

Numerade Educator

00:53

Problem 43

Determine how much money would be in a savings account that started with a deposit of $$\$ 2000$$ in year 1 with each succeeding amount increasing by $15 \%$ per year. Use an interest rate of $10 \%$ per year and a 7 -year time period.

Liuxi Sun

Numerade Educator

Problem 44

The future worth in year 10 of a decreasing geometric gradient series of cash flows was found to be $$\$ 80,000$$. If the interest rate was $10 \%$ per year and the annual rate of decrease was $8 \%$ per year, what was the cash flow amount in year 1 ?

Check back soon!

Problem 45

Altmax Ltd, a company that manufactures automobile wiring harnesses, has budgeted $$P=\$ 400,000$$ now to pay for a certain type of wire clip over the next 5 years. If the company expects the cost of the clips to increase by $4 \%$ each year, what is the expected cost in year 2 if the company uses and interest rate of $10 \%$ per year?

Check back soon!

Problem 46

Thomasville Furniture Industries offers several types of high-performance fabrics that are capable of withstanding chemicals as harsh as chlorine. A certain midwestern manufacturing company that uses fabric in several products has a report showing that the present worth of fabric purchases over a specific 5 -year period was $$\$ 900,000$$. If the costs are known to have increased geometrically by $5 \%$ per year during that time and the company uses an interest rate of $15 \%$ per year for investments, what was the cost of the fabric in year 1 ?

Check back soon!

01:42

Problem 47

Find the equivalent annual worth of a series of investments that starts at $$\$ 1000$$ in year 1 and increases by $10 \%$ per year for 15 years. Assume the interest rate is $10 \%$ per year.

Gregory Higby

Numerade Educator

01:15

Problem 48

A northern California consulting firm wants to start saving money for replacement of network servers. If the company invests $$\$ 5000$$ at the end of year 1 but decreases the amount invested by $5 \%$ each year, how much will be in the account 4 years from now, if it earns interest at a rate of $8 \%$ per year?

Nick Johnson

Numerade Educator

Problem 49

A company that manufactures purgable hydrogen sulfide monitors is planning to make deposits such that each one is $5 \%$ smaller 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.

Check back soon!

Problem 50

Akron Coating and Adhesives (ACA) produces a hot melt adhesive that provides a strong bond between metals and thermoplastics used for weather stripping, seals, gaskets, hand grips for tools, appliances, etc. ACA claims that by eliminating a primer coat, manufacturers can cut costs and reduce scrap. If Porter Cable is able to save $$\$ 60,000$$ now and $$\$ 50,000$$ per year by switching to the new adhesive, what is the present worth of the savings for 3 years at an interest rate of $10 \%$ per year?

Check back soon!

Problem 51

Attenuated Total Reflectance (ATR) is a method for looking at the surfaces of materials that are too opaque or too thick for standard transmission methods. A manufacturer of precision plastic parts estimates that ATR spectroscopy can save the company $$\$ 5000$$ per year by reducing returns of out-of-spec parts. What is the future worth of the savings if they start now and extend through year 5 at an interest rate of $10 \%$ per year?

Check back soon!

03:28

Problem 52

To improve crack detection in aircraft, the U.S. Air Force combined ultrasonic inspection procedures with laser heating to identify fatigue cracks. Early detection of cracks may reduce repair costs by as much as $$\$ 200,000$$ per year. If the savings start now and continue through year 5, what is the present worth of these savings at an interest rate of $10 \%$ per year?

Robin Corrigan

Numerade Educator

01:15

Problem 53

Some studies have shown that taller men tend to earn higher salaries than equally qualified men of shorter stature. Homotrope growth hormone can increase a child's height at a cost of $$\$ 50,000$$ per inch. Clyde's parents wanted him to be 3 inches taller than he was projected to be. They paid for the treatments for 3 years (at a cost of $$\$ 50,000$$ per year) beginning on their son's 8th birthday. How much extra money would Clyde have to earn per year from his 26th through 60th birthdays (a total of 35 years) in order to justify their expenditure at an interest rate of $8 \%$ per year?

Breanna Ollech

Numerade Educator

02:39

Problem 54

Calculate the annual worth (years 1 through 7) of Merchant Trucking Company's cash flow. Use an interest rate of $10 \%$ per year.
$$
\begin{array}{lrrrrrrrr}
\text { Year } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline \text { Cash Flow, \$ millions } & 450 & -40 & 200 & 200 & 200 & 200 & 200 & 200
\end{array}
$$

Vanna Tran

Numerade Educator

Problem 55

The by-product department of Iowa Packing utilizes a cooker that has the cost stream shown. Determine the present worth in year 0 of the costs at an interest rate of $10 \%$ per year.
$$
\begin{array}{cc}
\hline \text { Year } & \text { Cost } \mathbf{( \$ 1 0 0 0 )} \\
\hline 0 & 850 \\
1 & 300 \\
2 & 400 \\
3 & 400 \\
4 & 400 \\
5 & 500 \\
\hline
\end{array}
$$

Check back soon!

Problem 56

An entrepreneurial electrical engineer approached a large water utility with a proposal that promises to reduce the utility's power bill by at least $15 \%$ through installation of patented surge protectors. The proposal states that the engineer will not be paid for the first year, but beginning in year 2, she will receive three equal, annual payments that are equivalent to $60 \%$ of the power savings achieved in year 1 due to the protectors. Assuming that the utility's power bill of $$\$ 1$$ million per year is reduced by $15 \%$ after installation of the surge protectors, what will be the future worth in year 4 of the uniform payments to the engineer? Use an interest rate of $10 \%$ per year.

Check back soon!

Problem 57

Metropolitan Water utility is planning to upgrade its SCADA system for controlling well pumps, booster pumps, and disinfection equipment so that everything can be controlled from one site. The first phase will reduce labor and travel costs by $$\$ 31,000$$ per year. The second phase will reduce costs by $$\$ 20,000$$ per year. If phase I will occur in years 1 through 3 and phase II in years 4 through 8 , what is the equivalent annual worth (years 1 through 8 ) of the upgraded system at an interest rate of $8 \%$ per year?

Check back soon!

Problem 58

Infrared thermometers by Delta Thermal Products are compatible with type K thermocouples and can provide rapid non contact measurement capabilities at a cost of $$\$ 135$$ per unit. A small private electric utility company plans to purchase 100 of the thermometers now and 500 more 1 year from now if the anticipated savings in labor costs are realized. What would the future worth of the savings have to be 4 years from now in order to justify the equipment purchases at an interest rate of $12 \%$ per year?

Check back soon!

Problem 59

Encon Systems, Inc., sales revenues for its main product line are as shown. Calculate the equivalent annual worth (years 1-7) using an interest rate of $10 \%$ per year.
$$
\begin{array}{cccc}
\hline \text { Year } & \text { Revenue, } \mathbf{\$} & \text { Year } & \text { Revenue, } \mathbf{\$} \\
\hline 0 & 4,000,000 & 4 & 5,000,000 \\
1 & 4,000,000 & 5 & 5,000,000 \\
2 & 4,000,000 & 6 & 5,000,000 \\
3 & 4,000,000 & 7 & 5,000,000
\end{array}
$$

Check back soon!

01:33

Problem 60

Cisco's gross revenue (the percentage of revenue left after subtracting the cost of goods sold) was $70.1 \%$ of total revenue over a certain 4 -year period. If the total revenue per year was $$\$ 5.8$$ billion for the first 2 years and $$\$ 6.2$$ billion per year for the last 2, what was the future worth of the gross revenue in year 4 at an interest rate of $14 \%$ per year?

Nick Johnson

Numerade Educator

Problem 61

Calculate the annual worth in years 1 to 8 of the following series of incomes and expenses at an interest rate of $10 \%$ per year.
$$
\begin{array}{ccc}
\hline \text { Year } & \text { Income, \$ per year } & \text { Expense, \$ per year } \\
\hline 0 & & 20,000,000 \\
1-5 & 8,000,000 & 1,000,000 \\
6-8 & 9,000,000 & 2,000,000 \\
\hline
\end{array}
$$

Check back soon!

03:52

Problem 62

A supplier of certain suspension system parts for General Motors wants to have a contingency fund that it can draw on during down periods of the economy. The company wants to have $$\$ 15$$ million in the fund 5 years from now. If the company deposits $$\$ 1.5$$ million now, what uniform amount must it add at the end of each of the next 5 years to reach its goal if the fund earns a rate of return of $10 \%$ per year?

Narayan Hari

Numerade Educator

Problem 63

A rural utility company provides standby power to pumping stations using diesel-powered generators. An alternative has arisen whereby the utility could use a combination of wind and solar power to run its generators, but it will be a few years before the alternative energy systems are available. The utility estimates that the new systems will result in savings of $$\$ 15,000$$ per year for 3 years, starting 2 years from now, and $$\$ 25,000$$ per year for 4 more years after that (i.e., through year 8 ). At an interest rate of $8 \%$ per year, determine the equivalent annual worth (years 1-8) of the projected savings.

Check back soon!

Problem 64

A design-construct-operate (DSO) company signed a contract to operate certain industrial wastewater treatment plants for 10 years. The contract will pay the company $$\$ 2.5$$ million now and amounts increasing by $$\$ 250,000$$ each year through year 10. At an interest rate of $10 \%$ per year, what is the present worth (year 0 ) of the contract to the DSO company?

Check back soon!

Problem 65

Expenses associated with heating and cooling a large manufacturing facility owned by Nippon Steel are expected to increase according to an arithmetic gradient. If the cost is $$\$ 550,000$$ now (i.e., year 0 ) and the company expects the cost to increase by $$\$ 40,000$$ each year through year 12 , what is the equivalent annual worth in years $1-12$ of the energy costs at an interest rate of $10 \%$ per year?

Check back soon!

Problem 66

Lifetime Savings Accounts, known as LSAs, allow people to invest after-tax money without being taxed on any of the gains. If an engineer invests $$\$ 10,000$$ now and then increases his deposit by $$\$ 1000$$ each year through year 20 , how much will be in the account immediately after the last deposit, if the account grows by $12 \%$ per year?

Check back soon!

Problem 67

A software company that installs systems for inventory control using RFID technology spent $$\$ 600,000$$ per year for the past 3 years in developing its latest product. The company wants to recover its investment in 5 years beginning now. If the company signed a contract that will pay $$\$ 250,000$$ now and amounts increasing by a uniform amount each year through year 5 , how much must the increase be each year, if the company uses an interest rate of $15 \%$ per year?

Check back soon!

Problem 68

The future worth in year 8 for the cash flows shown in $$\$ 20,000$$. At an interest rate of $10 \%$ per year, what is the value $x$ of the cash flow in year 4 ?
Cash Flow can't copy

Check back soon!

Problem 69

The annual worth (years 1 through 8) of the cash flows shown is $$\$ 30,000$$. What is the amount $x$ of the cash flow in year 3, if the interest rate is $10 \%$ per year?
Cash Flow can't copy

Check back soon!

Problem 70

Levi Strauss has some of its jeans stone-washed under a contract with independent U.S. Garment Corp. If U.S. Garment's operating cost per machine is $$\$ 22,000$$ per year for years 1 and 2 and then it increases by $8 \%$ per year through year 10 , what is the equivalent uniform annual cost per machine (years 1-10) at an interest rate of $10 \%$ per year?

Check back soon!

Problem 71

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. Beginning 3 years from now, however, the costs are expected to increase by $10 \%$ per year into the foreseeable future (that is, $$\$ 12,650$$ in year 3 , $$\$ 13,915$$ in year 4 , etc.) If the railroad uses a 10 -year study period and an interest rate of $15 \%$ per year, how much could the railroad afford to spend now on the overpass in lieu of the maintenance contracts?

Check back soon!

Problem 72

Thunder Mountain Concrete and Building Materials is trying to bring the company-funded portion of its employee retirement fund into compliance with HB-301. The company has already deposited $$\$ 200,000$$ in each of the last 5 years. If the company increases its deposits (beginning in year 6) by $15 \%$ per year through year 20 , how much will be in the fund immediately after the last deposit, if the fund grows at a rate of $12 \%$ per year?

Check back soon!

Problem 73

San Antonio is considering various options 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 declining production will decrease revenue by $10 \%$ each year. If the aquifer will be totally depleted in 20 years, what is the present worth of the desalting option at an interest rate of $6 \%$ per year?

Check back soon!

01:12

Problem 74

Revenue from gas wells that have been in production for at least 5 years tends to follow a decreasing geometric gradient. One particular rights holder received royalties of $$\$ 4000$$ per year for years 1 through 6 , but beginning in year 7 , income decreased by $15 \%$ per year through year 14 . What was the future value (year 14) of the income from the well, if all of the income was invested at $10 \%$ per year?

Matt Just

Numerade Educator

Problem 75

An engineer conducting an economic analysis of wireless technology alternatives discovered that the $A / F$ factor values were not in his copy of the tables. Therefore, he decided to create the $(A / F, i, n)$ factor values himself. He did so by
a. multiplying the $(A / P, i, n)$ and $(P / F, i, n)$ values.
b. dividing $(P / F, i, n)$ values by $(P / A, i, n)$ values.
c. multiplying the $(P / A, i, n)$ and $(P / F, i, n)$ values.
d. multiplying the $(F / A, i, n)$ and $(P / F, i, n)$ values.

Check back soon!

Problem 76

The amount of money that would be accumulated in 12 years from an initial investment of $$\$ 1000$$ at an interest rate of $8 \%$ per year is closest to
a. $$\$ 2376$$.
b. $$\$ 2490$$.
c. $$\$ 2518$$.
d. $$\$ 2643$$.

Check back soon!

04:56

Problem 77

An executor for a wealthy person's estate discovered an uncollected note of $$\$ 100,000$$ dated July 10, 1973. At an interest rate of $6 \%$ per year, the value of the note on July 10, 2008, would be closest to
a. 684,060 .
b. $$\$ 725,100$$.
c. $$\$ 768,610$$.
d. $$\$ 814,725$$.

Puneet Prajapati

Numerade Educator

View

Problem 78

An engineer planning for retirement decides that she wants to have income of $$\$ 100,000$$ per year for 20 years with the first withdrawal beginning 30 years from now. If her retirement account earns interest at $8 \%$ per year, the annual amount she would have to deposit for 29 years beginning 1 year from now is closest to
a. $$\$ 7360$$.
b. $$\$ 8125$$.
c. $$\$ 8670$$.
d. $$\$ 9445$$.

Lauren Long

Numerade Educator

Problem 79

A winner of the Texas State lottery was given two choices: receive a single lump sum payment now of $$\$ 50$$ million or receive 21 uniform payments, with the first payment to be made now, and the rest to be made at the end of each of the next 20 years. At an interest rate of $4 \%$ per year, the amount of the 21 uniform payments that would be equivalent to the $$\$ 50$$ million lump-sum payment would be closest to
a. less than $$\$ 3,400,000$$.
b. $$\$ 3,426,900$$.
c. $$\$ 3,623,600$$.
d. $$\$ 3,923,800$$.

Check back soon!

Problem 80

A manufacturer of tygon tubing wants to have $$\$ 3,000,000$$ available 10 years from now so that a new product line can be initiated. If the company plans to deposit money each year, starting now, the equation that represents how much it will have to deposit each year at $8 \%$ per year interest in order to have the $$\$ 3,000,000$$ available immediately after the last deposit is made is
a. $3,000,000(A / F, 8 \%, 10)$
b. $3,000,000(A / F, 8 \%, 11)$
c. $3,000,000+3,000,000(A / F, 8 \%, 10)$
d. $3,000,000+3,000,000(A / F, 8 \%, 9)$

Check back soon!

Problem 81

The maker of a motion-sensing towel dispenser is considering adding new products to enhance offerings in the area of touchless technology. If the company does not expand its product line now, it will definitely do so in 3 years. Assume the interest rate is $10 \%$ per year. The amount the company can afford to spend now if the cost 3 years from now is estimated to be $$\$ 100,000$$ is
a. $$\$ 75,130$$.
b. $$\$ 82,640$$.
c. $$\$ 91,000$$.
d. $$\$ 93,280$$.

Check back soon!

Problem 82

Assume you borrow $$\$ 10,000$$ today and promise to repay the loan in two payments, one in year 2 and the other in year 5, with the one in year 5 being only half as large as the one in year 2. At an interest rate of $10 \%$ per year, the size of the payment in year 5 would be closest to
a. less than $$\$ 3900$$.
b. $$\$ 3975$$.
c. $$\$ 4398$$.
d. $$\$ 8796$$.

Check back soon!

Problem 83

If you borrow $$\$ 24,000$$ now at an interest rate of $10 \%$ per year and promise to repay the loan with payments of $$\$ 3000$$ per year starting one year from now, the number of payments that you will have to make is closest to
a. 8 .
b. 11 .
c. 14 .
d. 17.

Check back soon!

Problem 84

You deposit $$\$ 1000$$ now and you want the account to have a value as close to $$\$ 8870$$ as possible in year 20. Assume the account earns interest at $10 \%$ per year. The year in which you must make another deposit of $$\$ 1000$$ is
a. 6 .
b. 8 .
c. 10 .
d. 12 .

Check back soon!

Problem 85

Levi Strauss has some of its jeans stone-washed under a contract with independent U.S. Garment Corp. U.S. Garment's operating cost per machine is $$\$ 22,000$$ for year 1 and then it increases by $$\$ 1000$$ per year through year 5 . The equivalent uniform annual cost per machine (years 1-5) at an interest rate of $8 \%$ per year is closest to
a. $$\$ 23,850$$.
b. $$\$ 24,650$$.
c. $$\$ 25,930$$.
d. over $$\$ 26,000$$.

Check back soon!

Problem 86

At an interest rate of $8 \%$ per year, the present worth in year 0 of a lease that requires a payment of $$\$ 9,000$$ now and amounts increasing by $5 \%$ per year through year 7 is closest to
a. $$\$ 60,533$$.
b. $$\$ 65,376$$.
c. $$\$ 67,944$$.
d. $$\$ 69,328$$.

Check back soon!