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engineering economy
Engineering Economy 17th Global Edition William G. Sullivan ,Elin M. Wicks ,C. Patrick Koelling - Solutions
98. Mary’s credit card situation is out of control because she cannot afford to make her monthly payments.She has three credit cards with the following loan balances and APRs: Card 1, $4,500, 21%; Card 2, $5,700, 24%; and Card 3, $3,200, 18%. Interest compounds monthly on all loan balances. A
97. Determine the present equivalent value of the cash-flow diagram of Figure P4-97 (p. 212) when the annual interest rate, ik, varies as indicated. (4.13)
96. Will must make quarterly estimated income tax payments to the Internal Revenue Service. The amounts and timing of these payments are shown below. Also shown are the monthly interest rates that apply to each interval of time. What is the P-equivalent of Will’s payments on January 15?
95. Katy deposits $1,500 in a savings account that has a floating rate of interest. She plans to withdraw all her money in 5 years. In that period, the annual interest rate paid on deposits in this account changes several times—the interest rates in the next 5 years are 8%, 10%, 9%, 10%, and 10%
94. Alex purchases 100 stocks in a company that pay dividends of $10 every year for the next 5 years. However, the prevailing interest rates at which he can discount future earnings changes from 4% in the first 3 years to 6% in the next 2 years. What is the present value of the dividend income?
93. Consider an EOY geometric gradient, which lasts for 8 years, whose initial value at EOY one is $3,000 and¯f = 5% per year thereafter. Find the equivalent uniform gradient amount over the same period if the initial value of the cash flows at the end of year one is $1,000.Complete the following
92. Christine Parry sets up a fund to pay for her daughter’s education. She invests an initial principal amount in this account, which then pays out $30,000 per year for the next 4 years in order to cover tuition expenses. It also pays out money for living expenses for these 4 years, starting at
91. An electronic device is available that will reduce this year’s labor costs by $8,000. The equipment is expected to last for 10 years. Labor costs increase at a rate of 5% per year and the interest rate is 10% per year. (4.12)a. What is the maximum amount that we could justify spending for the
90. You invest 10% of your income into a savings product by paying annual deposits into the account, which earn an interest at the rate of 10% per year, but cannot be withdrawn. At the time of retirement, the savings product converts into a checking account paying 3% interest, but with no
89. It is likely that your college tuition will increase an average of 8% per year for the next 4 years.The annual cost of tuition at the beginning of your freshman year in college will be $12,000 (A1). How much money will you and your parents have to deposit in a mutual fund account one year prior
88. A small company heats its building and spends $10,000 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 12% per year starting one year from now (i.e., the first cash flow is $11,200 at EOY one). Their maintenance on the gas furnace is $565 per year, and
87. A geometric gradient that increases at ¯f = 6% per year for 15 years is shown in the accompanying diagram.The annual interest rate is 12%. What is the present equivalent value of this gradient? (4.12)
86. Start saving for retirement immediately! Even a modest amount will add up in a hurry. Jay decides to follow this advice and puts away 1% of his annual salary of $50,000 per year. This equates to $500 on his 21st birthday, and his salary will increase by 2% (on average)every year thereafter
85. You are the manager of a large crude-oil refinery. As part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. The replacement and downtime cost in the first year is $200,000. This cost is
84. A retail outlet is being designed in a strip mall in Nebraska. For this outlet, the installed fiberglass insulation to protect against heat loss in the winter and heat gain in the summer will cost an estimated$100,000. The annual savings in energy due to the insulation will be $24,000 at EOY
83. What value of N comes closest to making the left-hand cash-flow diagram of the accompanying figure, Figure P4-83 (p. 210), equivalent to the one on the right?Let i = 15% per year. Use a uniform gradient amount (G)in your solution. (4.11)
82. For the cash flows given below, determine the value of G that makes the present worth in year 0 equal to$2,000 if the interest rate is 6% per year. (4.11.4)Year 0 1 2 3 4 5 6 Cash 100 0 500 500 – G 500 – 2G 500 – 3G 500 – 4G Flow
81. Suppose that the parents of a young child decide to make annual deposits into a savings account, with the first deposit being made on the child’s fifth birthday and the last deposit being made on the 15th birthday. Then, starting on the child’s 18th birthday, the withdrawals as shown will
80. The following equation describes the conversion of a cash-flow diagram into an equivalent equal end-of-year series with N = 10. Given the equation, reconstruct the original cash-flow diagram. (4.11)A = [(800 + 20(A/G, 6%,7)](P/A, 6%, 7)(A/P, 6%, 10)+ [300(F/A, 6%,3)−−500](A/F, 6%, 10)
79. In the accompanying diagram, Figure P4-79, what is the value of K on the left-hand cash-flow diagram that is equivalent to the right-hand cash-flow diagram?Let i = 12% per year. (4.11)
78. You owe your best friend $3,000. Because you are short on cash, you offer to repay the loan over 24 months under the following condition. The first payment will be$100 at the end of month one. The second payment will be$100 + G at the end of month two. At the end of month three, you’ll repay
77. Refer to the accompanying cash-flow diagram (see Figure P4-77), and solve for the unknown quantity in Parts (a) through (d) that makes the equivalent value of cash outflows equal to the equivalent value of the cash inflow, F. (4.11)a. If F = $10,000, G = $600, and N = 6, then i = ?b. If F =
76. For a repayment schedule that starts at EOY 4 at$Z and proceeds for years 4 through 10 at $2Z, $3Z, . . . , what is the value of Z if the principal of this loan is$12,000 and the interest rate is 12% per year? Use a uniform gradient amount (G) in your solution. (4.11)
75. Suppose that annual income from a rental property is expected to start at $1,500 per year and decrease at a uniform amount of $50 each year after the first year for the 10- year expected life of the property. The investment cost is $7,000, and i is 8% per year. Is this a good investment? Assume
74. The nominal interest rate is 12% compounded semiannually. What amount will need to be deposited every six months to be able to have enough money to pay three annuity payments of $10,000 for three years beginning at the end of year seven? The deposits begin now and continue every six months
73. Determine the value of P0, as a function of H, for these two investment alternatives to be equivalent at an interest rate of i = 15% per year: (4.10)0 5 10 End of Year End of Year 1.7H H H 10 15 5 2P0 P0 10
72. Find the value of the unknown quantity, P0, that establishes equivalence in the cash-flow diagram below.Suppose i = 20% per year. Use an annuity factor and a uniform gradient factor in your solution. (4.10)$800$1,400$1,100$2,000$500 $500 $500 $500 $500 10 0P0 = ?1 2 3 4 5 6 7 8 9 End of Year
71. It costs $67,500 to retrofit the gasoline pumps at a certain filling station so the pumps can dispense E85 fuel(85% ethanol and 15% gasoline). If the station makes a profit of $0.10 per gallon from selling E85 and sells an average of 60,000 gallons of E85 per month, how many months will it take
70. Suppose $1,000 is deposited in a bank account today (time 0), followed by $1,000 deposits in years 2, 4, 6, and 8. At 6% annual interest, how much will the future equivalent be at the end of year 12? (4.10)
69. A company borrowed $120,000 at an interest rate of 9% to be repaid over a period of six years. The loan will be repaid in installments according to the cash-flow diagram shown below (which also reflects the cash inflow of $120,000). What is the size of the last payment (X)required to pay off
68. Determine the value ofW on the right-hand side of the accompanying diagram (see Figure P4-68) that makes the two cash-flow diagrams equivalent when i = 12% per year. (4.10)$1,000 $1,000 57 End of Year$1,000 End of Year W W 0 1 2 3 40
67. A corporation makes a payment of $2.25 million at the end of 2017 for services rendered by a large database company. With an annual interest rate of 15%, what annual payments at the end of years 2017 through 2022 will be equivalent to $2.25 million at the end of 2017? (4.10)
66. Suppose you have an opportunity to invest in a fund that pays 12% interest compounded annually. Today, you invest $10,000 into this fund. Three years later (EOY 3), you borrow $5,000 from a local bank at 10% annual interest and invest it in the fund. Two years later (EOY 5), you withdraw enough
65. Are the following cash-flow diagrams economically equivalent if the interest rate is 10% per year? (4.10)EOY EOY 5M 5M 5M 5M 3M 4M 5M 6M 0 1 2 3 4 0 1 2 3 4
64. A study by the New York Federal Reserve Bank concludes that an engineering bachelor’s degree generates approximately a 18% return on investment over the course of a decade. Suppose the typical engineering student spends $20,000 per year for four years on his/her education. What extra annual
63. The Turners have 12 years to save a lump-sum amount for their child’s college education. Today a four-year college education costs $80,000, and this is expected to increase by 8% per year into the foreseeable future. (4.10)a. If the Turners can earn 5% per year on a conservative investment in
62. You begin to save money to buy a car, which will be worth $25,000 five years from now. In order to buy this car, you pay a fixed amount of $X into your car savings fund, starting now for the next 4 years.a. Find $X, the value that must be deposited into the account, if the annual interest rate
61. It is estimated that you will pay about $100,000 into the social security system (FICA) over your 40- year work span. For simplicity, assume this is an annuity of $2,500 per year, starting with your 26th birthday and continuing through your 65th birthday. (4.10)a. What is the future equivalent
60. Maintenance expenses for a bridge on a local river are estimated to be $30,000 per year for the first 10 years, followed by two separate $80,000 expenditures in years 15 and 20. The expected life of the bridge is 30 years. If i = 7% per year, what is the equivalent uniform annual expense over
59. A transport company sets aside funds to maintain its trucks. It anticipates spending $3,000 on repairs in EOY 1, $2,000 in EOY 2, and $1,000 for the next 3 years.The interest rate is 10% per year. (4.10)a. What is the value of expenses if the interest rate is 0%?b. What is the present
58. Lisa plans to retire on her 65th birthday. On her 30th birthday, Lisa will start saving $A per year for 35 years. Starting on her 65th birthday, Lisa plans on withdrawing $15,000 and will continue these annual withdrawals until the account is exhausted on her 80th birthday. If Lisa’s bank
57. What lump sum of money must be deposited into a bank account at the present time so that $600 per month can be withdrawn for 5 years, with the first withdrawal scheduled for 5 years from today? The interest rate is 1/2%per month. (Hint: Monthly withdrawals begin at the end of the month 60.)
56. How much money should be deposited each year for 10 years if you wish to withdraw $400 each year for 6 years, beginning at the end of the 12th year? Let I = 5%per year. (4.9)
55. Leon and Heidi decided to invest $2,000 annually for only the first 8 years of their marriage. The first payment was made at age 30. If the annual interest rate is 8%, how much accumulated interest and principal will they have at age 68? (4.9)
54. Kris borrows some money during her senior year to buy a new car. The car dealership allows her to defer payments for 12 months, and Kris makes 60 end-of-month payments thereafter. If the original note (loan) is for $25,000 and interest is 0.75% per month on the unpaid balance, how much will
53. Suppose you drive a 2013 model automobile that averages 24 miles per gallon (mpg)for 12,000 miles annually. If you purchase a new automobile that averages 28 mpg, how much extra money can you afford, based on fuel savings, to invest in the new car? Your personal interest rate is 5% per year,
52. A financial consultant offers you a pension product that allows you to invest your retirement savings of$300,000 in a deposit that pays 4% per annum. At the same time, you can annually withdraw up to $25,000 from this savings pool. How many years will your savings last, if you were to withdraw
51. Today the average undergraduate student is responsible for paying off a $3,800 balance on his/her credit card. Suppose the monthly interest rate is 2% (24%APR). How many months will it take to repay the $3,800 balance, assuming monthly payments of $100 are made and no additional expenses are
50. Suppose that your rich uncle has $5,000,000 that he wishes to distribute to his heirs at the rate of $250,000 per year. If the $5,000,000 is deposited in a bank account that earns 4% interest per year, how many years will it take to completely deplete the account? How long will it take if the
49. Consider the accompanying cash-flow diagram.(See Figure P4-49.) (4.7)a. If P = $1,000, A = $200, and i% = 12% per year, then N = ?b. If P = $1,000, A = $200, and N = 10 years, then i = ?c. If A = $200, i% = 12% per year, and N = 5 years, then P = ?d. If P = $1,000, i% = 12% per year, and N = 5
48. If interest is 22% compounded quarterly, what is the amount that will be accumulated in a sinking fund at the end of 12 years if $250 is deposited in the fund at the beginning of each of the 12 years? (4.7.1)
47. The Golden Gate Bridge in San Francisco was financed with construction bonds sold for $35 million in 1931. These were 40- year bonds, and the $35 million principal plus almost $39 million in interest were repaid in total in 1971. If interest was repaid as a lump sum, what interest rate was paid
46. A piece of airport baggage-handling equipment can be purchased for $85,000 outright or for $90,000 to be financed over 48 months at 0% interest. This special offer is good for only the next two days. The salesperson states that at least $20,000 can be saved by the 0% offer compared to their
45. The cost to equip a large cruise ship with security cameras is $200,000. If the interest rate is 10% per year and the cameras have a life of 8 years, what is the equivalent annual cost (A) of the security cameras? (4.7)
44. The Dell Corporation borrowed $14,000,000 at 9% interest per year, which must be repaid in equal EOY amounts (including both interest and principal) over the next seven years. How much must Dell repay at the end of each year? How much of the total amount repaid is interest? (4.7)
43. A large automobile manufacturer has developed a continuous variable transmission(CVT) that provides smooth shifting and enhances fuel efficiency by 2 mpg of gasoline. The extra cost of a CVT is $1,000 on the sticker price of a new car. For a particular model averaging 24 miles per gallon with
42. A large electronic retailer is considering the purchase of software that will minimize shipping expenses in its supply chain network. This software, including installation and training, would be a $10-million investment for the retailer. If the firm’s effective interest rate is 15% per year
41. Engineering graduates earn $750,000 more than the average Liberal Arts BA holder in a career. Assume the$750,000 is a lump-sum equivalent at the end of a 35- year career. How much extra does the engineering grad earn per year if the interest rate is 5% per year? (4.7.3)
40. The engineering department at a leading university decides to implement an energy-saving program by reducing its usage of electricity for lighting and heating the department buildings. The department wants to save $300,000 at the end of 3 years.Electricity costs $0.25/kWh. (4.7)a. By how much
39. A 35- year-old person wants to accumulate$900,000 by age 75. How much will she need to save each month, starting one month from now, if the interest rate is 0.75% per month? (4.7)
38. The U.S. stock market has returned an average of about 9% per year since 1900. This return works out to a real return (i.e., adjusted for inflation) of approximately 6% per year. (4.7)a. If you invest $40,000 and you earn 6% a year on it, how much real purchasing power will you have in 40
37. The Surrey County board of supervisors has agreed to fund an ambitious project that will “spend money now to save much more money in the future.” A total of $16.2 million will be awarded to the Green Corporation for energy improvements in 40 buildings, 27 parks, and 37 traffic
36. A geothermal heat pump can save up to 80% of the annual heating and cooling bills of a certain home in the northeastern U.S. In this region, the yearly cost of conventionally heating and cooling a 2,500-square-foot house is about $3,000. With a federal tax credit of 35% on the total
35. Spivey just won a lottery! The $10,000,000 jackpot will be paid in 25 annual installments of $400,000 each, with the first payment to be paid immediately. Spivey’s opportunity cost of capital (interest rate) is 2% per year.What is the present equivalent of Spivey’s lottery winnings at the
34. A company is considering two investments: the first is an investment in equipment worth $70,000, which will reduce costs by $15,000 every year for the next 5 years.The second is an investment in human resource training, worth $40,000, which will reduce costs by $5,000 every year for the next 5
33. Automobiles of the future will most likely be manufactured largely with carbon fibers made from recycled plastics, wood pulp, and cellulose.Replacing half the ferrous metals in current automobiles could reduce a vehicle’s weight by 60% and fuel consumption by 30%. One impediment to using
32. An outright purchase of $30,000 now (a lump-sum payment) can be traded for 36 equal payments of $1,177 per month, starting one month from now. What is the monthly interest rate that establishes equivalence between these two payment plans? (4.7)
31. Twelve payments of $13,000 each are to be repaid at the end of each month. The monthly interest rate is 3%. (4.7)a. What is the present equivalent (i.e., P0) of these payments?b. Repeat Part (a) when the payments are made at the beginning of the month. Note that the present equivalent will be
30. Will has a 30- year mortgage on a $100,000 loan for his house in Florida. The interest rate on the loan is 6%per year (nominal interest), payable monthly at 0.5% per month. (4.7)a. What is Will’s monthly payment?b. If Will doubles his payment from Part (a), when will the loan be completely
29. Liam O’Kelly is 25 years old and is thinking about buying a term life insurance policy with his wife as the beneficiary. The quoted annual premium for Liam is $7.63 per thousand dollars of insurance coverage. Because Liam wants a $100,000 policy (which is 3.5 times his annual salary), the
28. Anna and Doug are in the market for a new house. The maximum payment they can afford is $900 per month. Of this payment, property taxes and homeowner’s insurance amount to $200 per month. If the interest rate on the mortgage is 6% per year, how expensive a house can Anna and Doug afford to
27. A credit card company wants your business. If you accept their offer and use their card, they will deposit 1% of your monetary transactions into a savings account that will earn a guaranteed 5% per year. If your annual transactions total an average of $20,000, how much will you have in this
26. Football coach Ira Blooper has just been fired as head coach at a large university. His buyout amount is $1.2 million, and Blooper will be repaid (as per his contract) in monthly installments over the next 2 years. If the interest rate is 2% per month, how much will Blooper receive each month?
25. Your parents make 25 equal annual deposits of$1,000 each into a bank account earning 4% interest per year. The first deposit will be made one year from today.How much money can be withdrawn from this account immediately after the 25th deposit? (4.7)
24. The Dominion Freight Company has invested$70,000 in a new sorting machine that is expected to produce a return of $8,500 per year for the next 10 years. At a 9% annual interest rate, is this investment worthwhile? (4.7)
23. The value of an investment comes from its cash flows. Let’s say you are intent on receiving $35,000 per year, starting at the end of year one and continuing over 10 years. A lump-sum of $330,000 invested now(year 0) will allow you to receive your desired annual amount. What interest rate is
22. In 1955, average annual earnings in the United States was $1,900, and in 2012, it was $42,700.What compound annual increase in earnings has been experienced over this period of time? If the consumer price index increased by 2.5% annually over the same period of time, would workers be in a
21. A good stock-based mutual fund should earn at least 10% per year over a long period of time. Consider the case of Barney and Lynn, who were overheard gloating(for all to hear) about how well they had done with their mutual fund investment. “We turned a $10,000 investment of money in 1985 into
20. In 1955, a 50- pound bag of onions cost 10 cents.The same bag is expected to cost $60 in 2014. What compounded annual increase in the cost of onions has been experienced over this period of time? (4.6)
19. In 2014, the average debt for college student loans is $32,300. This amounts to a $300 monthly payment for a “standard” loan repayment plan over 10 years. What monthly interest rate is being charged on this typical student loan? (4.6)
18. Calculate the compounded future value of 15 annual payments of $2,000 each into a savings account that earns 4% per year. All 15 payments are made at the beginning of each year. (4.6)
17. The monthly average cable TV bill in 2017 is$74.50. If cable costs are climbing at an annual rate of 7% per year, how much will the typical cable subscriber pay in 2024? (4.6)
16. Use the rule of 72 to determine how long it takes to accumulate $10,000 in a savings account when P = $5,000 and i = 10% per year. (4.6)Rule of 72: The time (years) required to double the value of a lump-sum investment that is allowed to compound is approximately 72 ÷ annual interest rate (as
15. Mr. Smith has saved $1,200 each year for 25 years.A year after the saving period ended, Mr. Smith withdrew $4,500 each year for a period of 5 years. In the sixth and seventh years, he only withdrew $3,000 per year. In the eighth year, he decided to withdraw the remaining money in his account.
14. Annie White graduated from college with a student-loan debt of $32,000. The interest rate on this debt is 0.5% per month. If monthly payments on this loan are $618.65, how many months will it take for Annie to repay the entire loan? (4.6)
13. You just inherited $12,000. While you plan to squander some of it away, how much should you deposit in an account earning 3% interest per year if you’d like to have $20,000 in the account in 20 years? (4.6)
12. A new oven will save $100 per year in electricity expense. How much can we afford to pay for this oven if it is expected to last 15 years? The interest rate is 12% per year. (4.7.2)
11. You have just invested a one-time amount of $6,000 in a stock-based mutual fund. This fund should earn (on average) 8% per year over a long period of time. How much will your investment be worth in 23 years? (4.6)
10. A lump-sum loan of $15,000 is needed by Chandra to pay for college expenses. She has obtained small consumer loans with 10% interest per year in the past to help pay for college. But her father has advised her to apply for a PLUS student loan charging only 7%interest per year. If the loan will
9. Suppose you contribute $12 per week ($624 a year) into an interest-bearing account that earns 7% a year (compounded once a year). That’s probably one less pizza per week! But if you contribute faithfully each week into this account, how much money would you have saved through the compounding
8. Jonathan borrowed $8,000 at 5% annual compound interest. He agreed to repay the loan with 5 equal annual payments at end-of-years 1–5. How much of the annual payment is interest, and howmuch principal is there in each annual payment? (4.4)
7. Refer to Plan 2 in Table 4- 1. This is the customary way to pay off loans on automobiles, house mortgages, etc. A friend of yours has financed $24,000 on the purchase of a new automobile, and the annual interest rate is 12% (1% per month). (4.4)a. Monthly payments over a 60- month loan period
6. An amount of $15,000 is borrowed from the bank at an annual interest rate of 12%.a. Calculate the equal end-of-year payments required to completely pay off the loan in four years.b. Calculate the repayment amounts if the loan ($15,000)will be repaid in two equal installments of $7,500 each, paid
5. How much interest is payable each year on a loan of$1,000 if the interest rate is 9% per year when half of the loan principal will be repaid as a lump sum at the end of 3 years and the other half will be repaid in one lump-sum amount at the end of 6 years? How much interest will be paid over the
4. Which investment yields the higher interest income:investing P dollars at 3% annual simple interest for 2 years or at 2% annual compound interest for 2 years? (4.2)
3. In Europe people are experiencing negative interest rates. This means banks charge their customers for protecting the patron’s money. If 10,000 euros (European Union currency) is deposited in a “savings” account that is subject to a negative interest rate of 1% per year, how much money
2. What is the future equivalent of $500 invested at 8%simple interest per year for 212 years? (4.2)
1. You want to take out a mortgage on a house worth$50,000, and pay it back in 10 years. Since your credit rating is very poor, the bank charges you simple interest at the rate of 2% per month. How much will you owe after 1 year? How much is the interest? (4.2)
41. A small textile plant was constructed in 2008. The major equipment, costs, and factors are shown below.Estimate the cost to build a new plant in 2018 if the index for this type of equipment has increased at an average rate of 12% per year for the past 10 years. Select the closest answer.
40. A car rental agency is considering a modification in its oil change procedure. Currently, it uses a Type X filter, which costs $5 and must be changed every 7,000 miles along with the oil (5 quarts). Between each oil change, one quart of oil must be added after each 1,000 miles. The proposed
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