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The following figures show the annual salaries in CHF of 20 GBS Mathematics of Finance
students doing Internship at Bank chains in Barcelona and Geneva.
Calculate the arithmetic mean, median, and mode Salary of the students.
15’180, 19’870, 14,375, 15’767, 15’870, 15’180, 14’375, 36’938, 15’180, 46’132,
15’525, 19’600, 14’375, 23’069, 16’767, 16’767, 17’880, 14’375, 14’375, 14’375

  1. Total 5% Marks:
    A Mathematics Investment analyst receives the following data showing the percentage
    changes in Labor costs of Junior managers in an investment bank Chain over a 12-months
    period. The highest change observed was +172 per cent for a senior manager in one of
    the banks in Madrid.
    Percentage Change Frequency
    -5 to under 0 2
    0 to under 5 32
    5 to under 10 25
    10 to under 15 10
    15 to under 20 8
    20 to under 25 3
    25 to under 30 2
    30 to under 35 5
    35 to under 40 4
    40 to under 100 3
    100 to 172 4
    a). What is the mean annual percentage change in Labor costs for Junior managers in
    this investment bank?
    b). What is the estimate of the Median Value? (3% Marks)
    c). What is the modal class interval? (2% marks)
  2. Total 5% Marks:
    The following information applies to a portfolio composed of Fund A and Fund B.
    Fund A Fund B
    Portfolio weights (%) 70 30
    Expected returns (%) 10 16
    Standard deviations
    7 13
    Correlation between
    the returns of Fund A
    and Fund B
    The portfolio’s standard deviation of return is closest to:
    A. 7.38%.
    B. 8.80%.
    C. 8.35%.
  3. Total 5% Marks:
    You open a bank account today (06th April 2022) expecting that your dad will credit
    your account three years later. If indeed your dad puts in CHF 15’500, how much
    money will have in your account after 10 years if your earn 6% interest semi-annually
  4. Total 5% Marks:
    Your dad has been asked to retire today and take his retirement benefits either as a
    lump sum or as an annuity. The pension officer presents him with two alternatives:
    ● An immediate lump sum of CHF 2 million
    ● An annuity with 20 payments of 200’000 each year starting today
    The interest rate at your bank is 7% per year annually compounded. Which option
    would you recommend your dad to take?
  5. Total 5% Marks:
    Your pension Fund manager estimates that the corporate sponsor will make CHF 10
    Million contributions, 5 years from now. The rate of return on the plan assets is
    estimated to be 9% per year. The Pension Fund manager wants to calculate the FV of
    this contribution 15 years from (the date at which the funds will be distributed to
    retirees). Compute that FV?
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