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    Normal Distribution, Time Value of Money

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    1.Consider the normal distributions drawn below (with different scales)

    They both have m = 20 and the area of the shaded region of each is 0.90. Which of the following holds?
    a. x1 < x2
    b. x1 > x2
    c. x1 = x2
    d. There is not enough information
    e. x1 >= x2

    2.If you deposit $5000 into a fund paying 6% interest compounded quarterly, how much can you withdraw at the end of each quarter for 5 years?
    a. $135.92
    b. $970.45
    c. $291.23
    d. $215.17
    e. none of the above

    Please see the attached file for full problem description.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:11 pm ad1c9bdddf
    https://brainmass.com/statistics/normal-distribution/normal-distribution-time-value-of-money-33826

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    SOLUTION This solution is FREE courtesy of BrainMass!

    1.Consider the normal distributions drawn below (with different scales)

    They both have m = 20 and the area of the shaded region of each is 0.90. Which of the following holds?
    a. x1 < x2
    b. x1 > x2
    c. x1 = x2
    d. There is not enough information
    e. x1 >= x2

    Answer: a. x1 < x2

    The standard deviation for b) s= 8 is greater than that of a) s= 5.
    This means that the spread around the mean is more for b) than for a)
    Thus x2 is farther from mean = M = 20.00
    Thus x1 < x2

    We can also calculate the numerical values of x1 and x2

    For x1
    Mean=M = 20.00
    Standard deviation =s= 5.00
    Z corresponding to 90% is 1.2816
    z=(x-M )/s or x=M +z*s
    or x1=20+1.2816*5= 26.41

    For x2
    Mean=M = 20.00
    Standard deviation =s= 8.00
    Z corresponding to 90% is 1.2816
    z=(x-M )/s or x=M +z*s
    or x2=20+1.2816*8= 30.25

    Therefore a. x1 < x2

    2.If you deposit $5000 into a fund paying 6% interest compounded quarterly, how much can you withdraw at the end of each quarter for 5 years?
    a. $135.92
    b. $970.45
    c. $291.23
    d. $215.17
    e. none of the above

    Answer: c. $291.23

    To calculate the amount that can be withdrawn each quarter we need to know PVIFA (Present Value Interest Factor for an Annuity)

    Withdrawal Q Quarterly
    No of years= 5
    No of Periods= 20 (=5 x 4 quarters per year)
    Discount rate annually= 6.00% annual
    Discount rate per period= 1.5% (= 6%/4)
    n= 20
    r= 1.5%

    PVIFA (20 periods, 1.5% rate=) 17.1686 (From the tables)

    Withdrawal (equal amount for each quarter):
    Present Value= 5,000 (The amount deposited at time t=0)
    Therefore
    withdrawal: 291.23 =5000/17.1686

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:11 pm ad1c9bdddf>
    https://brainmass.com/statistics/normal-distribution/normal-distribution-time-value-of-money-33826

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