CSP Math questions

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CSP Math questions
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  1. 312 = ____________ (Use the x2 key)
    961
  2. 18
  3. 304
    810,000
  4. Log 100
    2
  5. Antilog of 3
    1,000
  6. e-5
    .0067
  7. 5!
    120
  8. 1/0.02 = 0.02-1
    50
  9. Sin 30o
    .5
  10. Arcsine 0.5
    30
  11. (5.43 x 1012) x (6.78 x 107)
    3.68 x 1020
  12. 3.14
  13. What is probability of getting a “1” when rolling a die?
    1/6
  14. What is probability of not getting a “1” when rolling a die?
    5/6
  15. Getting a “1” or “2” in one roll of a die?
    1/3

    Solution: 1/6 + 1/6 = 2/6
  16. Getting “snake eyes” (both dies are 1) when rolling two die?
    1/36

    Solution: 1/6 x 1/6
  17. A machine produces 0.02 defective parts. The probability that none of ten parts sampled will be defective is?
    .82

    Solution: (.98)10
  18. A machine produces 0.02 defective parts. The probability that some of the 10 parts are defective is?
    .18

    Solution: Pf = 1 - .82
  19. A machine produces 0.02 defective parts. The probability that all of the 10 parts are defective is?
    1.02 x10-17

    Solution: (.02)10
  20. Determine the following based on these sample data: 8, 12, 25, 25, 28, 36, 41

    Median =
    25
  21. Determine the following based on these sample data: 8, 12, 25, 25, 28, 36, 41

    Mode =
    25
  22. Determine the following based on these sample data: 8, 12, 25, 25, 28, 36, 41

    Range =
    33
  23. Determine the following based on these sample data: 8, 12, 25, 25, 28, 36, 41

    Mean =
    25
  24. Determine the following based on these sample data: 8, 12, 25, 25, 28, 36, 41

    Sample Deviation =
    11.86
  25. Determine the following based on these sample data: 8, 12, 25, 25, 28, 36, 41

    Population Deviation =
    10.98
  26. What is the future value of a deposit of $5,000 if the interest rate is 10% and the time if 5 years?


    $8,052.55
  27. What is the present value (discount value) of the future sum of $10,000 if the interest rate is 10% and the time is 10 years?
     

    $3,855.43
  28. What is the future value of saving $100 per month if the interest rate is 6% and the time is 10 years?


    $16,387.93
  29. new machine for the production floor. Option one is to lease a new machine for 10 years at $2,000 per year. Option two is to purchase the machine for $10,000 with a maintenance agreement of $500 per year. After 10 years, you can sell the machine for a salvage value of $5,000. The value of money will be 15% for the ten years. Which option?
            

    • Lease = $10,037.5
    • Purchase = $11,273.5
  30. What is the present value of $10,000 five years from now if the interest rate is expected to be 7%?


    $7,129.86
  31. How much money should be in the bank if a one-time deposit of $20,000 is made and left for 20 years at 9%?


    $112,088.2
  32. What is the present value of an annuity that will pay $1,000 at the end of each of the next three years and the interest rate is 8.5%?


    $2,554
  33. How much money must be deposited today for the balance to equal $50,000 in 20 years if the interest rate is 7%?


    $12,920.95
  34. A five-part block and tackle is used to lift a load of 500 lbs. If the friction loss is 10% for each sheave, what force will be required?
        

    161.1
  35. The block and tackle in the previous problem is set to lift a load vertically 10 feet. How many feet must the operator pull to make this lift?
    50

    Solution: 5 x 10
  36. Given the following diagram, what is the compression in member BC?

    1,960 lbs

    Solution:
  37. Which members of the following truss are in compression?

    AB, BC, and CD

    Solution: Cat walks over, turtle walks under
  38. Which members of the following truss are in compression?

    AE, ED, EB, EC

    Solution: Cat walks over, turtle walks under
  39. What is the required pressure for a fire protection sprinkler with a K value of 5.6, protecting 120 ft2 with a density of 0.22 gpm per ft2?


    26.4 gpm
  40. How much pressure would be lost to friction for 200 ft of 6-inch steel pipe (i.e. 6.065 in) and providing a flow of 1,850 gpm? The C factor is 100.


    30.76 psi
  41. Given the following diagram, what is the minimum height of the dike required to contain the contents of the largest tank plus 10% allowance for precipitation? The tanks are 12 meters and 8 meters in diameter, and both are 8 meters high.

           

    1.69m
  42. A four foot by six foot container is ten feet deep and filled with 50% water and 50% oil by volume with a specific gravity of 0.8. What is the pressure one-half the distance from the surface if the oil and water remain separated?
    1.7 psi

    Solution: .8 x .433 x 5ft
  43. A four foot by six foot container is ten feet deep and filled with 50% water and 50% oil by volume with a specific gravity of 0.8. What is the pressure at the bottom of the tank if the oil and water remain separated?
    3.9 psi

    • Solution: .9 x .433 x 10ft
    • (1.0 + .8)/2 = .9
  44. A four foot by six foot container is ten feet deep and filled with 50% water and 50% oil by volume with a specific gravity of 0.8. What is the pressure at the bottom of the tank if the oil and water are mixed?
    3.9 psi

    • Solution: .9 x .433 x 10ft
    • (1.0 + .8)/2 = .9
  45. A submerged solid container with a mass of 500,000 kg is lifted from the bottom of a freshwater lake with a crane. The container is 4 meters by 6 meters by 10 meters high and rests vertically on the bottom. As the crane lifts the container from the lake, the cable breaks when 5 meters of the container is out of the water. What was the load on the cable when it failed?
    F = 3,724,000 N
  46. A container with a mass of 200 kg (440 lbs) falls off the back of a truck and slides 50 meters (165 feet) before coming to rest. The coefficient of friction is 0.3. How fast was the truck moving?


    62 km/hr
  47. In the diagram, the coefficient of friction is 0.5 between the 100 lbs box and the upper ramp, 0.3 between the 40 lbs box and the lower portion of the ramp, and the pulley is frictionless. As drawn, will the boxes remain on the ramp?

         

    3.2 Stay
  48. Given the following diagram, what is the total resistance?



    4.54 Omhs
  49. What is the total current?



    24.2 amps
  50. What is the current at Point B?



    11 amps
  51. A safety professional has collected the following data about a lifting task: H=25cm, V=75cm, and D=70cm, and the loads are lifted at the rate of four per minute for 90 minutes per shift. There is no angle of asymmetry. The coupling is rated as good. The boxes weigh 18 kg. According to NIOSH, find the LI?


    • LI = 1.23
    • RWL = 14.57
  52. a lifting task: H=25cm, V=75cm, and D=70cm, and the loads are lifted at the rate of four per minute for 90 minutes per shift. There is no angle of asymmetry. The coupling is rated as good. The boxes weigh 18 kg. According to NIOSH, find the LI?

    Now duration is only 45 minutes per shift. What is the new FM?
    .84
  53. A safety professional has collected the following data about a lifting task: H=25cm, V=75cm, and D=70cm, and the loads are lifted at the rate of four per minute for 90 minutes per shift. There is no angle of asymmetry. The coupling is rated as good. The boxes weigh 18 kg. According to NIOSH, find the LI?

    Now a rate of 3 lifts per minute. What is the new FM?
    .79
  54. A safety professional has collected the following data about a lifting task: H=25cm, V=35cm, and D=25cm, and the loads are lifted at the rate of six per minute for 4 hours per shift. There is no angle of asymmetry. The coupling is rated as good. The boxes weigh 18 kg, and the RWL is 10 kg. According to NIOSH, what is the LI?


    1.8
  55. Employee noise exposures for an eight-hour day are recorded as follows: 2 hrs at 90 dBA, 4 hrs at 95 dBA, and 2 hrs at 100 dBA. What is the TWA?
      

    TWA = 95.8 dBA
  56. Employee noise exposures for an eight-hour day are recorded as follows: 1 hr at 85 dBA, 4 hrs at 88 dBA, and 3 hrs at 91 dBA. What is the percent dose using a 3 decibel exchange rate if 85 dBA for 8 hours equals 100%?
       

    • D = 262.5%
    • TWA = 89.2 dBA
  57. Given the following diagram for a round duct system, what is the volume in cfm flowing through the Duct B?

               

    Q = 5,480 cfm
  58. The managers of a corporation are paid an average of $4,800 per month while the hourly work force averages $780 per week. The standard deviation of the managers salary is $820 and the workers is $64.
    There is more variation of the manager’s salaries than the workers

    Solution = Managers 820/4800 = .17 and Employees 64/780 = .08
  59. The BCSP has just released the latest exam results. The average score was 125 and the standard deviation 15. A group of 21 people took the ASP Preparation Workshop prior to the above exam. Their average score was 133 and the standard deviation was 11. Are the scores of the seminar participants significantly better than the average score at the p=0.05 level?


    t = 3.25

    Lookup on Pg 9 = (0.5 & 20) = 1.725

    Answer = YES
  60. Your facility made 1,000 widgets with an average life expectancy of 500 hours with a standard deviation of 100 hours. What percent of the widgets will fail in the first 225 hours?


    z = 2.75

    Lookup Pg 8 (2.7 & 5) = 0.4970

    Solution: 0.5 - 0.4970 = 0.003 or .3%
  61. Your facility made 1,000 widgets with an average life expectancy of 500 hours with a standard deviation of 100 hours. What percent of the widgets will fail in the first 225 hours?

    What is the probability of failure before 600 hours?
    84%

    Solution: 68/2 = 34, then 34+50 = 84%
  62. As the Safety Director of your company, you are concerned about the number of first aid and recordable cases involving new employees (less than one year of experience) versus the number of cases involving the more experienced employees. A survey of the employee incident/accident data reveals the following:



    Can you be 99% sure that any differences observed in the above data are not due to chance?


    • X2 = 8.18
    • Lookup table Pg 10 (p = 1-.99 = .01) 6.635
    • Answer = YES
  63. An airplane has two engines, each with a probability of success of 0.90. What is the probability that the airplane will arrive safely if one or both engines working will ensure a safe arrival?
    0.99
  64. A component has six parts connected in series, each with a probability of failure of 0.05. Determine the probability of component failure?
    0.26
  65. A widget is made of three components called wiglets. Wiglet ‘A’ has a 0.30 probability of success (Ps), wiglet ‘B’ has Ps of 0.45, and wiglet ‘C’ has Ps of 0.60. Calculate the Ps if wiglets B and C are functionally in parallel and wiglet A is in series.
    0.234

    Note: Pf you should multiply parallel, Ps you should multiply series
  66. A group of 20 chips are in a piece of equipment. What is the probability of two and only two chips failing if the chips are known to be 0.03 defective?


    P = 0.0988 or .1
  67. You have just bought a certificate of deposit for $10,000. If the APR is 5% and the time 5 years, how much interest will you make over the life of the CD if interest is compounded annually?


    • $2,762.8
    • Note: Don't forget to subtract initial COD
  68. You have set a personal goal to have one million dollars in savings in 30 years. How much will you have to save each year to meet this goal if the interest rate will be 8%?


    $8,827.4
  69. A new machine for the production area will reduce the cost of the hearing conservation program by $18,000 per year. The machine costs $100,000 and the maintenance expense will be $1,000 each year. If the interest rate is 8% and the machine will last 10 years, what is the annual cost benefit (savings) of purchasing the machine?
    $17,000
  70. A new machine for the production area will reduce the cost of the hearing conservation program by $18,000 per year. The machine costs $100,000 and the maintenance expense will be $1,000 each year. If the interest rate is 8% and the machine will last 10 years, what is the maximum amount the company should pay for this machine?


    $114,071.38
  71. The initial cost of a safety project will be $10,000. This project costs $2,000 per year to maintain, but will save the company $4,000 each year over its life expectancy of 6 years at 7%. Should the company invest in the startup?


    P = $9,533.08

    Answer = NO (10,000>9,533)
  72. You have borrowed money to train all employees in hazardous waste disposal procedures. The balloon payment of $14,000 is due in 4 years. If the interest rate is 12%, how much should you deposit each year if you are going to meet the balloon payment?


    $2,929.28
  73. The expected value of a contract is defined as the most representative value of a group of data, yet does not have to be one of the data points. What is the expected value of the contract if the contract proposal has the flowing probability of profit (loss)?

    $43,250
  74. How many widgets must be manufactured to cover a loss of $100,000 due to an employee injury if the widgets sell for $100 and the profit is 10% on each widget?
    10,000

    Solution: 100 x .1 = 10, then 105 / 10 = 104
  75. How many widgets must be manufactured to cover a loss of $100,000 due to an employee injury if the widgets sell for $100 and the profit is 10% on each widget?

    What is the total dollars in sales to produce this same $100,000?
    1,000,000

    Solution: 100 x .1 = 10, then 105 x 10 = 106
  76. What is your annual return on investment if you spend $10,000 on a safety improvement plan, and after one year, the calculated return to the company is $10,750?


    ROI = 7.5%
  77. A company records 24 cases in 2009 which are classified as recordable for their record keeping process. If the company uses an index rate of 100 employees at 40 hours per week and 50 weeks per year, what is the calculated annual incident rate for 950,000 hours?


    TRIR = 5.05
  78. The total resistance in a circuit with parallel resistors of 10, 15, and 20 ohms is


    4.6 ohms
  79. A 2,000 lbs load is suspended by a 2-leg sling. Each leg of the sling makes a 60o angle with the load. The tension in each leg of the sling is
    1,154.7 lbs
  80. A machine produces defective parts at a rate of .05 (5%). The probability that none of eight parts sampled being defective is
    .66

    Solution: 1-.05 =.95, then (.95)8
  81. A machine produces defective parts at a rate of .05 (5%). The probability that all eight parts sampled being defective is
    3.9 x 10-11

    Solution: (.05)8
  82. A machine produces defective parts at a rate of .05 (5%). The probability that one or more of the eight parts sampled being defective is
    .34

    Solution: 1-.66
  83. What is the probability that none of the students will have a birthday in March (40 students)?
    .03

    Solution: (11/12)40
  84. What is the probability that all of the students will have a birthday in March (40 students)?
    6.8 x 10-44

    Solution: (1/12)40
  85. What is the probability that at least one of the students will have a birthday in March (40 students)?
    .97

    Solution: 1-.03

  86. The percent of students scoring between 105 and 135 is
    68%

  87. The percent of students scoring between 75 and 165 is
    99.7%

  88. The percent of students scoring over 135 is
    16%

  89. The percentile ranking of a student that scored 150 is
    97.5%

    Solution: 95 + 5/2

  90. If your score on the BCSP exam was 126, the percent of those taking the exam that did better than you is
    34.46

    • Solution: 6/15=.4 from the table is .1554, then 34 - 15.54=18.46
    • 100-95=5/2=2.5
    • 95-68=27/2=13.5
    • 2.5 + 13.5 + 18.46 = 34.46

  91. If 450 people took the exam, the number of people that did better than you is (note: use 34.46% as # that did better than you)
    155

    Solution: 450 x .3446
  92. 11, 12, 12, 13, 14, 15, 17
     Mode =
     Median = 
     Range = 
     Mean = 
     Sample standard deviation =
     Population standard deviation =
    • Mode = 12
    • Median =  13
    • Range =  6
    • Mean =  13.4
    • Sample standard deviation =  2.07
    • Population standard deviation = 1.92
  93. How much would a box weigh if it took 20 lbs of force to push/pull the box along a level floor and the coefficient of friction (µ) is .5?


    40 lbs
  94. A box weighing 40 pounds is on a ramp with a 20% grade. Will the box remain on the ramp if the coefficient of friction (µ) is .5?
    Yes

    • Solution: Tan B = 20/100
    • Cos 11.31 = Fy/40 = 39.22, then 39.22 x .5 = 19.61
    • Sin 11.31 = Fx/40 = 7.8
    • 19.61 > 7.8 (downward force more than sliding force)
  95. If car weighting 3,500 lbs can stop in 100 ft and the µ was .2, what was the initial velocity of the car?


    24.49 mph
  96. A tool is being sharpened on an 8 in grinding wheel operating at 500 rpm. The tool jams in the tool rest and is thrown away from the wheel with an initial velocity of?
    1047.2 fpm

    • V = C x rpm
  97. A tank weighing 25,000 pounds (shell & contents) is going to be placed on an elevated platform which has a maximum loading of 50 lbs/ft2. What is the minimum diameter of the tank that will not exceed the platform load rating?
      

    25.2 ft (Note: convert r to d)
  98. What is the current (amps) at point B in the diagram?


    11 amps
  99. A standpipe 75 ft high with a radius of 3 inches is filled with water. The pressure at the bottom of the standpipe is


    32.48 psi

    Solution: .433 x 75 x 1
  100. What velocity head would be needed to produce a water flow of 100 ft/second?


    155.27 ft
  101. A secondary containment structure contains three tanks (one w/35’ diameter and two w/20’ diameter). If the inside dimensions of the perimeter concrete dike are 50’ x 80’ x 4’, the capacity available to contain the contents of the largest tank is? _______ gal
       

    100,881 gal
  102. A secondary containment structure contains three tanks (one w/35’ diameter and two w/20’ diameter). If the inside dimensions of the perimeter concrete dike are 50’ x 80’, the capacity available to contain the contents of the largest tank is 101,000 gal, what is the height of the wall?
    4 ft
  103. If you are using a two-piece block and tackle with five parts of rope to lift a weight of 2,500 pounds, how many pounds of force are required for a dynamic lifting condition? (Assume friction is 10% each time the rope crosses a pulley (sheave) and negating the weight of the block and tackle)


    805.3 lbs
  104. Given a safety factor of 10 for 1/2” manila rope with a tensile strength of 1,500 lbs, what is the maximum safe working load?


    150
  105. What is the lifting index (LI) of a task when: H=10in, V=30in, D=30in, A=0o, F=4 lift/min, C=good, work duration 90 minutes, and the load is 40 pounds?
    1.24
  106. If you have four machines operating in an area with dB levels of 90, 95, 93 & 100, what is the combined sound pressure level?
    102 dBA
  107. You record a reading of 120 dBA with a sound level meter at a distance of 10 ft from a compressor. If you  move to a distance of 20 ft from the compressor, the noise level reading will be?
    114 dBA
  108. According to OSHA, how long can an employee be exposed to continuous noise levels of 110 DB?


    30 mins
  109. An employee working around a compressor has his noise exposure monitored with a dosimeter. If the dosimeter reading is 400% for an eight hour shift, the TWA in decibels is


    100 dBA
  110. Coefficient of entry (Ce) is a measure of the efficiency of a hood’s ability to convert static pressure to velocity pressure; the ratio of actual flow to ideal flow. What is the Ce if VP = 1.5 and SPh = -2.0?


    .87
  111. What is the capture velocity 6” from the opening of an unflanged 6” duct if the face velocity is 150 fpm?
    11.25 fpm

    Solution: 150 x 7.5%
  112. Determine the volume flow rate in a 6 in diameter duct where the total pressure is -0.8” and the static pressure is -2.5”? ____cfm
       

    5,222 cfm
  113. You have identified the following outdoor temperature readings: wet bulb 28oC, globe 31oC, dry bulb 25oC. The WBGT is __________oC


    28.3 oC
  114. 1.             Given that the half-value layer thickness for Cesium-137 in concrete is 5.33 cm (2.1 in). What radiation reading would be anticipated if one foot of concrete is placed between a source and the monitoring instrument that previously read 40 mR/hr? ___________ mR/hr
    .77 mR/hr

    Solution: 12in/2.1in = 5.7 hvl, then 40 x .55.7 = .77
  115. Your company has average worker compensation losses of $50,000/yr over the past 10 yrs. The consulting firm promises to reduce these losses by 50% (to $25,000/yr) over the next decade if you sign a contract. The terms of the contract require an initial payment of $100,000 and an annual retainer of $10,000 for each of the 10 years of the contract. Assume an annual interest rate of 6%. Accept or Decline?


    Accept

    Solution: 50k-25k-10k=15k, then subtract 100k initial payment
  116. Given the equation P = X3 (X1 +X2) for a valve failure, and the following values, what is the probability of the valve working?
    X1 = .0025    X2 = .0015    X3  = .0050
    1 - Pf = Ps

    .99998
  117. An airplane has two engines, each with a Pf of .1 per flight. If the airplane can operate safely with only one engine, what is the Ps on a given flight?
    .99

    Solution: 1-(.1)2
  118. A component has three parts connected in series, each with a failure probability 0.1. failure of any part causes the component to fail. Determine the probability of component failure.
    .27

    Solution: 1-(.9)3
  119. An employee receives 67% of their daily dose to a contaminant in 3hr 15mins. What will this employee’s dose be after 8 hours at this same level of exposure?
    165

    Solution: 3.25/8 = 67/x, x=165
  120. What would the worker compensation premium be for an employee that earned $1,000, worked in a classification with a manual rating of 3.50, and the experience modification was 1.15?
    40.25

    Solution: 1000/100=10, 10 x 3.5 x 1.15=40.25
  121. A company with 6 OSHA recordables injuries and 130,000 hours of exposure last year had a TCIR of?
    9.2

    Solution: (#rec/hours)*200,000
  122. A company with 34 cases involving days away from work and 33 cases involving restricted work days and 1000 full time employees has an annual DART incident rate of?
    6.7

    Solution: (#days away or restricted/hours)*200,000. 1000 employees work 2000 hours = 2,000,000 hours. 34+33 = 67
  123. Painter A takes 3 days to paint the Smith house. Painter B takes 5 days to pain the same house. If both painter work together, how long will it take them to pain the Smith house?
    1.875

    Hint:Inverse formula
  124. A component may fail if either subcomponent x or y fails. If x has a probability of failure of .5 and y has a probability of .7, what is the overall probability that the component will fail?
    .85

    Solution: .5+.7-(.5x.7)
  125. New analytical equipment is being purchased for $25,000. Investigation now shows that the operating costs and maintenance will be $600 per year more than the manufacturer has guaranteed. If the expected life is eight years and the cost of money is 8%, how much should be deducted from the purchase price to compensate for the extra operating costs?


    $3,447.98
  126. A 250-stone weights 150kg when submerged in water? The specific gravity of the stone is?
    2.5

    Solution: 250-150=100, 250/100=2.5
  127. A cylinder of dry air (molecular weight of 28.8) has a volume of 44.8 liters and is filled to a pressure of 2,250 lb/in2 at 0oC. The mass of air in the cylinder is?


    8.7 kg (Hint: convert from g to kg)
  128. The larger thank is 40ft in diameter and 23 ft high. The smaller is 26 ft in diameter and 18 ft high. diked area must be increased to 110% of the capacity of the largest tank. The volumes of the tanks are 28,888 ft3 and 9,552 ft3, respectively. The dike is masonry construction in rectangular shape, 90 ft x 75 ft. How high must the dike be?
    5.1 ft

    Solution: Area of dike - area of small tank=6219.1, Volumn +10% / remaining area
  129. In the design of presence-sensing, point-of-operation device for a press, what is the minimum distance required from the sensing field to the point-of-operation, assuming a hand speed constant of 63 inches/sec and a stopping time for the press of .75 sec?
    47.25

  130. What is the power consumed by this direct-current circuit?
     

    7.7

    (Hint: P can also =I2R)
  131. A new safety system can be designed and installed for $2,000,000. Because of this investment, annual property losses are expected to decrease about $195,000 calculated at the end of the first full year the new system was installed. The life of the new safety system is 25 years, and the expected interest rate is associated with the cost of money is 8%, compounded annually. What is the net present value of this new safety system?


    $81,581.36

    (Hint: don't forget to subtract initial investment)
  132. A capital investment of $10,000 was made exactly 5 years ago. This investment was placed in a financial instrument with a 3% annual percentage rate, compounded monthly. When the investment principal and interest proceeds are withdrawn, what is the total return on investment of the initial investment of $10,000?


    16%

    • Solution: Use ROI formula = F-intial/intial=.16 or 16%
    • Hint: interest rate is compounded monthly
  133. A large heavy construction project lasted exactly 6 years, from the project’s start-up to the project’s wrap-up. Safety professionals conducted weekly inspections of the construction site using the same inspection protocol over the entire 6-year period. Assuming a normal distribution, what is the best estimate of the number of inspections that had inspection scores within plus or minus 1 standard deviation of the mean?
    212

    • Solution: 6x52=312, then 312 x .68 = 212
    • Hint: 68% is middle section of the bell curve
  134. The total direct and indirect costs of a loss total $100,000. How many units sold for $1.00 each must a self-insured company manufacture to recover this cost assuming that the profit margin on each unit is 10%?
    1,000,000

    Solution: $100,000 x 10 = $1,000,000/$1 = 1,000,000
  135. A wealth relative recently died and left you her estate. You can choose to either accept $6,000,000 today or wait and receive $10,000,000 in five years. Assuming the annual interest rate over this period is 10% you should? _____________accept $6mil or $10mil?



    Accept $10 million

    Solution: $10mil is greater than $9.6 mil over the 5 years

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