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engineering economy
Engineering Economy 17th Edition William Sullivan, Elin Wicks, C Koelling - Solutions
4-120. What is the present equivalent of a uniform series of annual payments of $3,500 each for five years if the interest rate, compounded continuously, is 10%? (4.16)
4-119. A person needs $18,000 immediately as a down payment on a new home. Suppose that she can borrow this money from her company credit union. She will be required to repay the loan in equal payments made every six months over the next 12 years. The annual interest rate being charged is 10%
4-118. A man deposited $10,000 in a savings account when his son was born. The nominal interest rate was 8% per year, compounded continuously. On the son’s 18th birthday, the accumulated sum is withdrawn from the account. How much will this accumulated amount be? (4.16)
4-117. Juan deposits $5,000 into a savings account that pays 7.2% per year, continuously compounded. What is the effective annual interest rate? Determine the value of his account at the end of two years. (4.16)
4-116. Find the value of the unknown quantity Z in the following diagram, such that the equivalent cash outflow equals the equivalent cash inflows when r = 20% compounded continuously: (4.16) Z Z 0 1 A $500/year Years 23456789
4-115. If a nominal interest rate of 8% is compounded continuously, determine the unknown quantity in each of the following situations: (4.16)a. What uniform EOY amount for 10 years is equivalent to $8,000 at EOY 10?b. What is the present equivalent value of $1,000 per year for 12 years?c. What is
4-114. College students are now graduating with loan debts averaging $24,000. (4.15, 4.16)a. If students repay their loan of $24,000 over 10 years with an annual effective interest rate of 8.3%, what will their annual payment be?b. What is the annual payment going to be when the interest rate is
4-113. Sarah is going to borrow money for her college expenses. Her local credit union will lend Sarah $15,000 now at a nominal interest rate of 4% per year, compounded quarterly. Then after two years, the credit union will lend her an additional $15,000 at a higher interest rate of 6% per year
4-112. The PHC is offering a prize of $5,000 per week for four years. If the interest rate is 5.2%, compounded weekly, what is the present equivalent value of the prize? What is the future equivalent value at the end of four years? (4.15)
4-111. Suppose you owe $1,100 on your credit card. The annual percentage rate (APR) is 18%, compounded monthly. The credit card company says your minimum monthly payment is $19.80. (4.15)a. If you make only this minimum payment, how long will it take for you to repay the $1,100 balance (assuming no
4-110. The average college graduate owes $22,500 in loans incurred over his/her college career. Now that it is so difficult to land a job after graduation, an option for the graduate seeking relief is to stretch the loan over 20 years (with the bank’s approval, of course) instead of repaying the
4-109. A financial institution offers a nominal interest rate of 12% while compounding its accounts quarterly. For how many years must quarterly deposits of $1,000 be made into this account so that $42,931 will be accumulated at the end of this time? (4.15.2)
4-108. Many people get ready for retirement by depositing money into a monthly or annual savings plan. (4.15)a. If $300 per month is deposited in a bank account paying a 6% APR compounded monthly, how much will be accumulated in the account after 30 years?b. If inflation is expected to average 2%
4-107. The monthly income from a piece of commercial property is $1,200. Annual expenses are $3,000 for upkeep of the property and $1,000 for property taxes. The property is surrounded by a security fence that cost $4,000 to install four years ago. (4.5, 4.6, 4.14)a. If i = 12% per year (the MARR)
4-106. You are making $100 monthly deposits into a savings account that pays interest at a nominal rate of 3% per year, compounded monthly. What is the future equivalent value of this account after five years? (4.15)
4-105. An automobile salesperson states that his company will pay the interest for the first 12 months of your automobile loan if you buy the vehicle today. Suppose you go ahead and purchase a car for $25,000 and finance it with a 48-month loan having an APR of 9%. What is your monthly payment
4-104. A friend of yours who had taken an engineering economy course stated that paying on a student loan even before graduation will give you a big break on the total loan costs. She cites the following example to illustrate her point. A student takes out a $10,000 loan for their freshman year of
4-103. Determine the amount of money that must be invested now (time 0) at 6% nominal interest, compounded monthly, to provide an annuity of $10,000 per year for 10 years, starting eight years from now. The interest rate remains constant over this entire period of time. (4.9, 4.15)
4-102. John Doe received the following information in a mailed advertisement: “You could borrow $4,250 for just $176.71 per month for 36 months at 28.4% APR. Get the money you need at a payment you can afford.” Would you take this borrowing opportunity? If not, what is the difficulty with it?
4-101. The winner of a state lottery will receive $30,000 a month for the rest of his/her life. Suppose the person who wins is 30 years old and has a life expectancy of 80 years. The monthly payments will be placed in a savings account that earns 0.25% per month (3% nominal interest per year,
4-100. Find the interest rates in the following situations. (4.14)a. APR = 8%, compounded monthly. Find the effective annual interest rate.b. Nominal rate is 10% compounded quarterly. Find the effective semi-annual rate.c. The effective annual interest rate is 11.02% and compounding is monthly.
4-99. You deposit $2,500 at the end of the year (k = 0) into an account that pays interest at a rate of 7% compounded annually. Two years after your deposit, the savings account interest rate changes to 12% nominal interest compounded monthly. Five years after your deposit, the savings account
4-98. 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
4-97. Determine the present equivalent value of the cash-flow diagram of Figure P4-97 (p. 182) when the annual interest rate, ik, varies as indicated. (4.13)
4-96. 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? (4.13)
4-95. A cash-flow series is increasing geometrically at the rate of 8% per year. The initial payment at EOY 1 is $5,000, with increasing annual payments ending at EOY 20. The interest rate is 15% compounded annually for the first seven years and 5% compounded annually for the remaining 13 years.
4-94. The Stafford plan now offers student loans at 4% annual interest. After two years the interest rate will increase to 6% per year. If you borrow $5,000 now and $5,000 each year thereafter for a total of four installments of $5,000 each, how much will you owe at the end of the fourth year?
4-93. Suppose you start saving for retirement when you are 45 years old. You invest $5,000 the first year and increase this amount by 3% each year to match inflation for a total of 20 years. The interest rate is 10% per year. How much money will you have saved when you are 65 years old? (4.12)
4-92. An amount, P, must be invested now to allow withdrawals of $1,000 per year for the next 15 years and to permit $300 to be withdrawn starting at the end of year 6 and continuing over the remainder of the 15-year period as the $300 increases by 6% per year thereafter. That is, the withdrawal
4-91. 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
4-90. Amy Parker, a 22-year-old and newly hired marine biologist, is quick to admit that she does not plan to keep close tabs on how her 401(k) retirement plan will grow with time. This sort of thing does not really interest her. Amy’s contribution, plus that of her employer, amounts to $2,200
4-89. 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
4-88. A small company heats its building and spends $8,000 per year on natural gas for this purpose. Cost increases of natural gas are expected to be 10% per year starting one year from now (i.e., the first cash flow is $8,800 at EOY one). Their maintenance on the gas furnace is $345 per year, and
4-87. 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)
4-86. 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
4-85. 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 $175,000. This cost is
4-84. 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 $18,000 at EOY
4-83. What value of N comes closest to making the left-hand cash-flow diagram of the accompanying figure, Figure P4-83 (p. 180), equivalent to the one on the right? Let i = 15% per year. Use a uniform gradient amount (G) in your solution. (4.11)
4-82. 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
4-81. 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
4-80. 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%,
4-79. 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)
4-78. You owe your best friend $2,000. Because you are short on cash, you offer to repay the loan over 12 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
4-77. 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 =
4-76. For a repayment schedule that starts at EOY four 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 $10,000 and the interest rate is 7% per year? Use a uniform gradient amount (G) in your solution. (4.11)
4-75. Suppose that annual income from a rental property is expected to start at $1,300 per year and decrease at a uniform amount of $50 each year after the first year for the 15-year expected life of the property. The investment cost is $8,000, and i is 9% per year. Is this a good investment?
4-74. 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
4-73. 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
4-72. 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)
4-71. It costs $30,000 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 $0.08 per gallon from selling E85 and sells an average of 20,000 gallons of E85 per month, how many months will it
4-70. 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)
4-69. 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
4-68. Determine the value of W 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)
4-67. A corporation makes a payment of $1.25 million at the end of 2017 for services rendered by a large database company. With an annual interest rate of 18%, what annual payments at the end of years 2017 through 2022 will be equivalent to $1.25 million at the end of 2017? (4.10)
4-66. 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
4-65. Are the following cash-flow diagrams economically equivalent if the interest rate is 10% per year? (4.10)
4-64. A study by the New York Federal Reserve Bank concludes that an engineering bachelor’s degree generates approximately a 15% return on investment over the course of a decade. Suppose the typical engineering student spends $15,000 per year for four years on his/her education. What extra annual
4-63. The Turners have 10 years to save a lump-sum amount for their child’s college education. Today a four-year college education costs $75,000, and this is expected to increase by 10% per year into the foreseeable future. (4.10)a. If the Turners can earn 6% per year on a conservative investment
4-62. A person deposits $1,000 in an account each year for five years (starting at the end of year one). At the end of the fifth year, one-half of the account balance is withdrawn; $2,000 is deposited annually for five more years (starting in the sixth year), with the total balance withdrawn at the
4-61. Suppose you are now 20 years old. You decide to save $A per year starting on your 21st birthday and continuing through your 60th birthday. At age 60 you will have saved an accumulated (compounded) amount of $F. A friend of yours waits five years to start her savings plan. It takes annual
4-60. A company is considering investing $10,000 in a heat exchanger. The heat exchanger will last five years, at which time it will be sold for $2,000. The maintenance cost at the end of the first year is estimated to be $1,000. Maintenance costs for the exchanger are estimated to increase by $500
4-59. A sum of $10,000 now (time 0) is equivalent to the following cash-flow diagram: What is the value of $B if the annual interest rate is 4%? (4.10)
4-58. Lisa plans to retire on her 61st birthday. On her 22nd birthday, Lisa will start saving $A per year for 40 years. Starting on her 62nd birthday, Lisa plans on withdrawing $10,000 and will continue these annual withdrawals until the account is exhausted on her 85th birthday. If Lisa’s bank
4-57. John is a very cost-conscious investor. His rule of thumb is that it costs $250 per year, starting in the first year of vehicle life to maintain an automobile. This expense increases by $250 each year over the life of the car. John is now considering the purchase of a five-year-old car with
4-56. How much money should be deposited annually in a bank account for five years if you wish to withdraw $5,000 each year for three years, beginning five years after the last deposit? The interest rate is 3% per year. (4.9)
4-55. Leon and Heidi decided to invest $3,000 annually for only the first eight years of their marriage. The first payment was made at age 25. If the annual interest rate is 10%, how much accumulated interest and principal will they have at age 65? (4.9)
4-54. Kris borrows some money in her senior year to buy a new car. The car dealership allows her to defer payments for 12 months, and Kris makes 48 end-of-month payments thereafter. If the original note (loan) is for $28,000 and interest in 0.5% per month on the unpaid balance, how much will
4-53. DuPont claims that its synthetic composites will replace metals in the construction of future automobiles. “The fuel mileage will double,” says DuPont. Suppose the light and stronger “composite automobile” will get 50 miles per gallon of gasoline, and the gasoline costs $3.50 per
4-52. Sarah’s wealth is now $1 million. She plans to withdraw 4% of her current wealth (i.e., $40,000) each year to maintain her current lifestyle. If she can earn 3% on her investment, for how many years can she live her current lifestyle before her money runs out? (4.7.5)
4-51. Today the average undergraduate student is responsible for paying off a $3,500 balance on his/her credit card. Suppose the monthly interest rate is 1.75% (21% APR). How many months will it take to repay the $3,500 balance, assuming monthly payments of $100 are made and no additional expenses
4-50. Stafford loans are the most popular form of student loan in the United States. The current interest rate on a Stafford loan is 4.67% per year. If you borrow $30,000 to help pay for your college education at the beginning of your freshman year, how much will you have to pay at the end of your
4-49. 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 =
4-48. If interest is 15% compounded quarterly, what is the amount that will be accumulated in a sinking fund at the end of 10 years if $100 is deposited in the fund at the beginning of each of the 10 years? (4.7.1)
4-47. 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
4-46. A piece of airport baggage handling equipment can be purchased for $80,000 cash or for $84,000 to be financed over 60 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
4-45. The cost to equip a large cruise ship with security cameras is $500,000. If the interest rate is 15% per year and the cameras have a life of six years, what is the equivalent annual cost (A) of the security cameras? (4.7)
4-44. The Dell Corporation borrowed $10,000,000 at 7% interest per year, which must be repaid in equal EOY amounts (including both interest and principal) over the next six years. How much must Dell repay at the end of each year? How much of the total amount repaid is interest? (4.7)
4-43. 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 $800 on the sticker price of a new car. For a particular model averaging 28 miles per gallon with
4-42. 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
4-41. 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)
4-40. Qwest Airlines has implemented a program to recycle all plastic drink cups used on their aircraft. Their goal is to generate $5 million by the end of the recycle program’s five-year life. Each recycled cup can be sold for $0.005 (1/2 cent). (4.7)a. How many cups must be recycled annually
4-39. Determine the P/A factor for i= 7.75% and N = 10 years. (4.7.2)
4-38. 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 $100,000 and you earn 6% a year on it, how much real purchasing power will you have in 30
4-37. The Anderson 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 York Corporation for energy improvements in 40 buildings, 27 parks, and 37 traffic
4-36. 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 2,000 square foot house is about $2,500. With a federal tax credit of 30% on the total
4-35. A $20,000 ordinary life insurance policy for a 22-year-old female can be obtained for annual premiums of approximately $250. This type of policy (ordinary life) would pay a death benefit of $20,000 in exchange for the annual premium paid during the lifetime of the insured person. If the
4-34. It is estimated that a certain piece of equipment can save $22,000 per year in labor and materials costs. The equipment has an expected life of five years and no market value. If the company must earn a 15% annual return on such investments, how much could be justified now for the purchase of
4-33. 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
4-32. An outright purchase of $20,000 now (a lump-sum payment) can be traded for 24 equal payments of $941.47 per month, starting one month from now. What is the monthly interest rate that establishes equivalence between these two payment plans? (4.7)
4-31. A 22-year-old college graduate just got a job in Nashville. She is considering buying a house with a $200,000 mortgage. The APR is 4% compounded monthly for her monthly mortgage payments on a 30-year fixed rate loan. If she can get her FICO score up to 750, the APR drops to 3.6%. How much in
4-30. 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
4-29. Liam O’Kelly is 20 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 $8.48 per thousand dollars of insurance coverage. Because Liam wants a $100,000 policy (which is 2.5 times his annual salary), the
4-28. Anna and Doug are in the market for a new house. The maximum payment they can afford is $700 per month. Of this payment, property taxes and homeowner’s insurance amount to $150 per month. If the interest rate on the mortgage is 4.5% per year, how much house can Anna and Doug afford to
4-27. 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
4-26. A father wants to know “How do I invest $50,000 now so that my daughter gets $1,000 per month of income for the next 10 years?” Calculate the answer for this dad. (4.7.2)
4-25. Your parents make 20 equal annual deposits of $2,000 each into a bank account earning 3% 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 20th deposit? (4.7)
4-24. Refer to the following cash-flow diagram. If i = 12% per year, what is P0 when N → ∞ (4.7.2)
4-23. An oil and gas producing company owns 45,000 acres of land in a southeastern state. It operates 650 wells which produce 21,000 barrels of oil per year and 1.5 million cubic feet of natural gas per year. The revenue from the oil is $2,100,000 per year and for natural gas the annual revenue is
4-22. In 1972 the maximum earnings of a worker subject to Social Security tax (SST) was $9,000. The maximum earnings subject to SST in 2016 is $118,500. What compound annual increase has been experienced over this 44-year period of time? How does it compare with a 3% annual increase in the consumer
4-21. 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 $25,000 investment of money in 1982
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