PS4: Problem 4 » Solution

[aranthe]

PS4 » Problem 4

def findMaxExpenses(salary, save, preRetireGrowthRates, postRetireGrowthRates,
                    epsilon):

    assert salary > 0, 'Salary must be greater than 0:' + str(salary)
    assert 0 < save < 100, 'Savings percentage must be between 0 and 100:' + str(savePct)
    assert 0 < epsilon < 1 , 'Upper boundary must be between 0 and 1:' + str(epsilon)

    # Generate the savings record.
    savingsRecord = nestEggVariable(salary, save, preRetireGrowthRates)

    # Savings at retirement will be the last entry;
    # it is also the upper limit on possible expenses.
    savingsAtRetirement = savingsRecord[-1]
    high = savingsAtRetirement
    guess = high # Seed initial guess.
    low = 0.0 # Seed lower guessing limit.
    found = False # Initialize search check.
    count = 1 # Initialize a counter, so search doesn't get out of hand.

    # Upper limit on count protects against process overruns.
    while not found and count < 100:

        # Calculate the fund balance with the current guess.
        fundBalances = postRetirement(savingsAtRetirement, postRetireGrowthRates, guess)
        endingBalance = fundBalances[-1] # Obtain the ending balance for testing.

        # Check to see if it is within episilon on either side of 0.
        if abs(endingBalance) < epsilon:
            found = True
        else:
            # If not, check to see if it's too high or too low.
            if endingBalance < 0:
                # Guess was too high. I need a new guess halfway between
                # the old one and the low.
                high = guess
                guess = (low + high)/2
            else:
                # Guess was too low. I need a new guess halfway between
                # the old guess and the last high.
                low = guess
                guess = (low + high)/2
            count = count + 1
    return guess