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fundamentals engineering economics

Questions and Answers of Fundamentals Engineering Economics

98. A series of 25 end-of-year deposits is made that begins with $1,000 at the end of year 1 and increases at the rate of $200 per year with a 12% interest rate compounded annually.a. What amount can
97. In Problem 94, with an interest rate of 6%, what increasing gradient series is equivalent to the cash fl ow profi le shown if the gradient series sought has a value of X at EOY 5 1 and a value of
96. In Problem 94, using an interest rate of 8%, what single sum of money occurring at the end-of-year 8 is equivalent to the cash fl ow profi le shown?
95. In Problem 94, using an interest rate of 10%, what uniform series over the closed interval [1,8] is equivalent to the cash fl ow profi le shown?
94. Consider the following cash fl ow profi le:What is the present worth equivalent for the cash fl ow series with an interest rate of 12%? 0 01234 $12,000 $11,000 $10,000 667 Cash Flow EOY Cash Flow
93. Consider a loan of $10,000 and the following pattern of cash fl ows.a. What is the interest rate that makes the present worth equal to $0.00?b. Using the interest rate determined in part (a), and
92. In Problem 90, suppose the positive-valued cash fl ows are replaced by a positive gradient series. If the cash fl ow at end-of-year 8 is $10,000, what gradient step is required for the cash fl ow
91. In Problem 90, what uniform annual series over [4,7] will be equivalent to the cash fl ow profi le if money is worth 6% compounded annually?
90. Consider the following cash fl ow profi le:With a compounded annual interest rate of 6%, what single sum of money at the end of the sixth year will be equivalent to the cash fl ow series? EOY 0 1
89. A series of 10 end-of-year deposits is made that begins with $7,000 at the end of year 1 and decreases at the rate of $300 per year with 10% interest.a. What amount could be withdrawn at t 5 10b.
88. A $90,000 investment is made. Over a 5-year period, a return of $30,000 occurs at the end of the fi rst year. Each successive year yields a return that is $3,000 less than the previous year’s
87. A person you trust foresees the need for a loan and suggests that you loan them $2,000 at the end of year 1, $1,000 at the end of year 2, nothing in year 3, and then they will pay you $1,000 in
86. Consider the following cash fl ow profi le:Using a gradient series factor, determine the present worth equivalent for the cash fl ow series using an annual compound interest rate of:a. 6%b. 7%
85. You want to be able to withdraw from a savings account $800 at the end of year 1, $900 at the end of year 2, $1,000 at the end of year 3, and so on over a total of 5 years. How much money must be
84. Video Solution Deposits are made at the end of years 1 through 7 into an account paying 6% per year interest. The deposits start at $5,000 and increase by $1,000 each year. How much will be in
83. A small company wishes to set up a fund that can be used for technology purchases over the next 6 years. Their forecast is for $12,000 to be needed at the end of year 1, decreasing by $2,000 each
82. Solve problem 81 for the case in which each successive payment is $700 less than the previous payment.
81. John borrows $10,000 at 18 percent compounded annually. He pays off the loan over a 5-year period with annual payments. Each successive payment is$700 greater than the previous payment. How much
80. Develop a single spreadsheet that allows you to calculate the PZG, FZG, and AZG factors. For each cell where the calculation is performed, place above it a small “control panel” that allows
79. On Juan’s 26th birthday, he deposited $7,500 in a retirement account.Each year thereafter he deposited $1,000 more than the previous year. Using a gradient series factor, determine how much was
78. Develop a mathematical relationship for fi nding the accumulated amount F at the end of n years that will result from a series of n beginning-of-year payments each equal to B if these payments
77. You have $20,000 that you put on deposit on your 30th birthday at 5% compounded annually. On your 40th birthday, the account begins earning 6%. Then, on your 50th birthday it begins earning 7%.
76. You deposit $X in an account on your 25th, 30th, and 35th birthdays. The account pays 9%. You intend to withdraw your savings in 10 equal annual withdrawals on your 41st, 42nd, . . . , 50th
75. Fishing Designs has arranged to borrow $15,000 today at 12% interest.The loan is to be repaid with end-of-year payments of $3,000 at the end of years 1 through 4. At the end of year 5, the
74. Determine the equivalent annual cash fl ow of this series at 10% interest: End of Year Cash End of Cash Flow Year Flow 0 1 2 -$2,500 $3,000 $4,500 66 5 $0 7 -$1,000 $7,000 34 3 $0 8 $3,000 4
73. In planning for your retirement, you have decided that you would like to be able to withdraw $60,000 per year for a 10 year period. The fi rst withdrawal will occur 20 years from today.a. What
72. Video Solution You decide to open an IRS approved retirement account at your local brokerage fi rm. Your best estimate is that it will earn 9%. At the end of each year for the next 25 years, you
71. How much money can be withdrawn at the end of the investment period if:a. $4,000 is invested at the end of each of 3 years at 5%/year compounded annually, with the lump sum then shifted into an
70. How much money can be withdrawn at the end of 15 years if:a. $2,000 is deposited at the end of each year and earns 5%/year compounded annually?b. $3,000 is deposited at the end of each year for
69. You plan to open a retirement account. Your employer will match 50% of your deposits up to a limit on the match of $2,500 per year. You believe the fund will earn 12% over the next 30 years, and
68. Janie deposits $10,000 in the bank today. Starting 3 years from now, she makes equal withdrawals of $1,000 for 5 years and then withdraws the remaining amount 10 years from now. How much will she
67. What uniform series over the interval [1,8] will be equivalent to a uniform series of $10,000 cash fl ows over the interval [3,10] based on:a. A 6% interest rate?b. A 10% interest rate?
66. What uniform series over the interval [11,20] will be equivalent to a uniform series of $10,000 cash fl ows over the interval [1,10] based on:a. A 6% interest rate?b. A 10% interest rate?
65. You take out a loan to build a swimming pool in the back yard of your new home. Your equal annual payments are 1/6th of the amount you borrowed.If it will take you 7 years to fully repay the
64. You take out a loan to buy a new audio system. Your equal annual payments are 20% of the amount you borrowed. The interest rate on the loan is 7%compounded annually.a. Determine the number of
63. You deposit $1,000 in a fund at the end of each year for a 10-year period.The fund pays 5% compounded annually. How much money is available to withdraw immediately after your last deposit?
62. You purchase a house for $250,000 directly from the buyer who owns the home outright. You pay a 20% down payment. You sign a fi rst mortgage and the buyer agrees to fi nance the remaining
61. An amount equal to $50,000 is borrowed at 7% annual compound interest.a. What size equal annual payment is required if the fi rst of 5 payments is made one year after receiving the $50,000?b.
60. If annual deposits of $1,000 are made into a fund paying 12 percent interest compounded annually, how much money will be in the fund immediately after the 5th deposit?
59. Adriana wishes to accumulate $2,000,000 in 35 years. If 35 end-of-year deposits are made into an account that pays interest at a rate of 7% compounded annually, what size deposit is required each
58. Eight equal deposits of $1,000 are made at the end of each year into a fund paying 8%.a. What is the present worth, 1 year before the fi rst deposit?b. What is the future worth, immediately after
57. What equal annual deposits must be made at t 5 2, 3, 4, 5, and 6 in order to accumulate $25,000 at t 5 8 if money is worth 10 percent compounded annually?
56. Juan borrows $25,000 at 7% compounded annually. If the loan is repaid in fi ve equal annual payments, what will be the size of Juan’s payments if the fi rst payment is made one year after
55. Determine the present worth of 5 equal annual deposits of $1,200 at the end of years 1 through 5, followed by 4 equal annual withdrawals of $700 at the end of years 4 through 7. Note that both
54. If money is worth more than 0% to you, would you rather receive $10,000/year for 5 years or receive $5,000/year for 10 years? What is your preference if you must pay these amounts, rather than
53. GO Tutorial Using a 5% annual compound interest rate, what investment today is needed in order to withdraw $5,000 annually:a. For 10 years?b. For 10 years if the fi rst withdrawal does not occur
52. Five deposits of $500 each are made a t 5 1, 2, 3, 4, and 5 into a fund paying 6 percent compounded per period. How much will be accumulated in the fund at (a) t 5 5, and (b) t 5 10?
51. Each and every year $7,500 is invested at 4% annual compound interest.a. What is the value of the investment portfolio after 20 years? After 25 years?After 30 years?b. Repeat part (a) if the
50. Jason has been making equal annual payments of $7,500 to repay a college loan. He wishes to pay off the loan immediately after having made an annual payment. He has eight payments remaining. With
49. Develop a single spreadsheet that allows you to calculate any of the PZA, AZP FZA, or AZF, factors. For each cell where the calculation is performed, place above it a small “control panel”
48. A debt of $1,000 is incurred at t 5 0. What is the amount of four equal payments at t 5 1, 2, 3, and 4 that will repay the debt if money is worth 10 percent compounded per period?
47. Juan deposits $1,000 in a savings account that pays 8 percent compounded annually. Exactly 2 years later he deposits $3,000; 2 years later he deposits$4,000; and 4 years later he withdraws all of
46. Maria deposits $1,200, $500, and $2,000 at t 5 1, 2, and 3, respectively. If the fund pays 8 percent compounded per period, what sum will be accumulated in the fund at (a) t 5 3, and (b) t 5 6?
45. Ken loans his grandson Rex $20,000 at 5.5% per year to help pay for executive chef schooling in Florida. Rex requires 3 years of schooling before beginning to earn a salary. He agrees to pay Ken
44. The manager at a Sherwin-Williams store has decided to purchase a new$30,000 paint mixing machine with high-tech instrumentation for matching color and other components. The machine may be paid
43. The cash fl ow profi le for an investment is given below and the interest rate is 8% compounded annually.a. Find the present worth of this series using the actual cash fl ows.b. Find the future
42. Renaldo borrows $8,000 from his aunt today to help pay for college expenses.He agrees to repay the loan according to the following schedule, at a rate of 6%/year compounded annually.a. Draw the
41. Ben deposits $5,000 now into an account that earns 7.5% interest compounded annually. He then deposits $1,000 per year at the end of the 1st and 2nd years. How much will the account contain 10
40. Video Solution An investment has the following cash fl ow series where interest is 8%:a. Determine the present worth of the series.b. Determine the future worth of the series at the end of the
39. If you invest $2,000 today, withdraw $1,000 in 3 years, deposit $3,000 in 5 years, deposit $1,500 in 8 years, and withdraw the entire sum three years after the fi nal deposit, how much will you
38. The cash fl ow profi le for an investment is given below and the interest rate is 6.5% compounded annually.a. Find the future worth of this cash fl ow series using the actual cash fl ows.b. Find
37. If a fund pays 12 percent compounded annually, what single deposit now will accumulate $12,000 at the end of the 10th year? If the fund pays 6 percent compounded annually, what single deposit now
36. You want to withdraw a single sum amount of $6,000 from an account at the end of 7 years. This withdrawal will zero out the account. What single sum of money deposited today is required if the
35. How much money today is equivalent to $10,000 in 12 years, with interest at 10% compounded annually?
34. Jason takes out a loan at 10% compounded annually for 7 years. At the end of this period, he pays off the loan at a value of $23,384.61. What amount did he borrow?
33. Calculate using the interest formula the factor (PZF11.5%,37). Compare that to the result obtained using Excel®’s PV function.
32. What is the present value of the following future receipts?a. $19,000 5 years from now at 9% compounded annuallyb. $8,300 12 years from now at 15% compounded annuallyc. $6,200 53 years from now
31. For your 21st birthday, your grandfather offers you a gift of $1,000 today. However, you have the choice of waiting 3 years and receiving $1,500 or waiting 5 years and receiving $3,000. If your
30. Video Solution What present amount of money must be deposited at 11% interest compounded annually to grow to $15,000 in 9 years? Give your answer to the nearest penny.a. Use the tables provided
29. GO Tutorial What deposit today is required for it to be worth $150,000 in 25 years if the deposit earns 5% annual compound interest?
28. How much money would have to be deposited today to accumulate:a. $10,000 after 6 years if the investment earns 5%/year compounded annually?b. $6,500 after 4 years if the investment earns 8%/year
27. Charlotte wishes to accumulate $100,000 in a savings account in 10 years.If she wishes to make a single deposit today and the bank pays 4% compounded annually on deposits of this size, how much
26. Develop a single spreadsheet that allows you to calculate FZP and PZF factors.For each cell where the calculation is performed, place above it a small“control panel” that allows you to enter
25. What rate of interest compounded annually is involved if:a. An investment of $10,000 made now will, 10 years from now, result in a receipt of $23,674?b. An investment of $2,000 made 18 years ago
24. How long, to the nearest year, does it take an investment at 6% compounded annually to (approximately):a. Double itself?b. Triple itself?c. Quadruple itself?
23. What will be the amount accumulated by each of the following present investments?a. $3,000 invested for 7 years at 14% compounded annually.b. $1,600 invested for 17 years at 12% compounded
22. If you invest $1,500 today and withdraw $2,500 in 3 years, what interest rate was earned?
21. How much money can be withdrawn at the end of the investment period if:a. $1,000 is invested at 8%/year compounded annually for 10 years?b. $5,000 is invested at 11%/year compounded annually for
20. At what interest rate will money:a. Double itself in 10 years?b. Triple itself in 10 years?c. Quadruple itself in 10 years?
19. With interest at 9% compounded annually, what is the fewest number of years (integer-valued) required for money to double in magnitude?
18. Video Solution You purchase a quarter section (160 acres) of land for$176,000 today and sell it in exactly 9 years for $525,000 at auction. At what annual compound rate did the value of your land
17. What is the smallest integer-valued annual compound interest that will result in an investment tripling in value in less than or equal to 10 years?
16. On August 1, 1958, fi rst-class postage for a 1-ounce envelope was 4¢. On August 1, 2007, a fi rst-class stamp for the same envelope cost 41¢. What annual compound increase in the cost of fi
15. Use the six approaches from Example 2.4 to determine to the nearest year how long it takes for an investment to double if the interest is compounded annually at the following rates.a. 5%d. 15%b.
14. Video Solution How much will a $25,000 investment today be worth in 10 years if it earns 7% annual compound interest?
13. If you deposit $5,000 4 years from today, how much will you be able to withdraw 10 years from today if interest is 8.5% per year compounded annually?
12. Video Solution Today you borrow $10,000 to pay for your expected college costs over the next four years, including a master’s degree. Two years from now, you determine that you need an
11. Draw a cash fl ow diagram depicting the net cash fl ows associated with the purchase, operation, and disposition of a synthetic rubber blending machine.The cash fl ow components are shown below.
10. Video Solution David is borrowing $150,000 from Hartford Bank to open Road and Off-Road Bicycle Shop. David expects it to take a few years before the shop earns a sizeable profi t, so he has
9. GO Tutorial Kaelyn borrows $30,000 from her grandfather today to cover her college expenses. She agrees to repay the loan, with the fi rst payment due 5 years from today in the amount of $2,000.
8. Video Solution You rent an apartment for $550 per month, payable at the beginning of the month. An initial deposit of $450 is required. Utilities are an additional $150 per month payable at the
7. Rodeo Jeans are stonewashed under a contract with independent USA Denim Company. USA Denim purchased two semiautomatic machines that cost$19,000 each at (t 5 0). Annual operating and maintenance
6. A laser cutting machine is purchased today for $23,000. There are no maintenance costs for the next two years. Maintenance at the end of year 3 is expected to be $2,000, with each subsequent
5. Pooi Phan needs $2,000 to pay off her bills. She borrows this amount from a bank with plans to pay it back over the next four years at $X per year. Draw a cash fl ow diagram from the bank’s
4. State the four DCF rules.
3. What words comprise the abbreviation “DCF”? Tell/describe/defi ne what it means in 10 words or less.
2. You are offered $500 now plus $500 one year from now. You can earn 6% per year on your money.a. It is suggested that a single fair amount be paid now. What do you consider fair?b. It is suggested
1. You are offered $200 now plus $100 a year from now for your used computer. Since the sum of those two amounts is $300, the buyer suggests simply waiting and giving you $300 a year from now. You
13. A child receives $100,000 as a gift which is deposited in a 6% bank account compounded semiannually. If $5,000 is withdrawn at the end of each half year, how long will the money last?a. 21.0
12. Under what circumstances are the effective annual interest rate and the period interest rate equal?a. Neverb. If the number of compounding periods per year is onec. If the number of compounding

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