MIT 6.0001 Problem Set 1C Solutions

1c.py

# MIT OCW 6.0001
# PSET 1C
# SOLUTION

# salary
starting_annual_salary = int(input("Starting salary? "))
# starting_annual_salary = 10000
semi_annual_raise = 0.07

# investments
annual_rate = 0.04
monthly_rate = annual_rate / 12

# target savings
down_payment_percentage = 0.25
house_price = 10**6
target_savings = house_price * down_payment_percentage

# how close is acceptable?
acceptable_diff = 100

# bisection
upper_bound = 1.0
lower_bound = 0.0
steps = 0

diff_from_target = target_savings * 2 # initialize to anything much larger than target savings
percentage_saved = 0.5

# while not yet in acceptable range
while abs(diff_from_target) > acceptable_diff and steps < 100:
    percentage_saved = (upper_bound + lower_bound) / 2

    annual_salary = starting_annual_salary
    current_savings = 0
    months_passed = 0

    # figure out savings over 36 months
    while months_passed < 36:
        monthly_salary = annual_salary / 12
        current_savings += current_savings * monthly_rate
        current_savings += percentage_saved * monthly_salary
        months_passed += 1

        # raise salary every 6 months
        if months_passed % 6 == 0:
            annual_salary += annual_salary * semi_annual_raise

    diff_from_target = target_savings - current_savings

    # saved too little!
    if diff_from_target > 0:
        lower_bound = percentage_saved
    # saved too much!
    elif diff_from_target < 0:
        upper_bound = percentage_saved

    steps += 1

else: # this "else" is for the while loop when it exits (look this up)
    if abs(diff_from_target) <= acceptable_diff:
        # {0:.4f} means replace with the argument at index 0 and round to 4 digits (:.4f)
        # {1} means replace with the argument at index 1
        print("%: {0:.4f}, steps: {1}".format(percentage_saved, steps))
    else:
        print("Not possible! :~(")