在二等分搜索中如何修复无限循环

Question

My code passes test cases but if anything about ~949,000 is input it enters an infinite loop.

I need to calculate the best rate at which to save a portion of a monthly income to save in order to afford a down payment in 36 months with 2 significant digits. I'm thinking this has something to do with me not quite understanding how epsilon is calculated - I've tried calculating epsilon as 0.0001 * total_cost, 0.0004 * portion_down_payment, and 0.0001 * annual_income all to no avail.

#House Hunting ps1c

low = int(0)
high = int(10000)
percent_saved = (low + high)/2.0

current_savings = 0
annual_salary = int(input("What is your starting anual salary? "))
total_cost = 1000000
semi_annual_raise = 0.07
portion_down_payment = total_cost * 0.25
epsilon = 100

r = 0.04

total_months = 0
steps = 0
while True:
    current_savings = 0
    monthly_salary = annual_salary/12
    for i in range(1,37):
        current_savings += (current_savings*r/12)
        current_savings += (monthly_salary * (percent_saved / 10000))     
        total_months += 1
        if total_months % 6 == 0:
            monthly_salary += monthly_salary * semi_annual_raise
    steps +=1   

    if abs(current_savings - portion_down_payment) <= epsilon:
        print("Steps in bisectional search: ", steps)
        best_savings_rate = str(percent_saved / 100)
        print("Best savings rate: ", (best_savings_rate + "%"))
        break
    elif (portion_down_payment - 100) - current_savings > 0:
        low = percent_saved
        percent_saved = int((low + high) / 2.0)
    else:
        high = percent_saved       
        percent_saved = int((low + high) / 2.0)

    if percent_saved >= 9999:
        print("It is not possible to afford this in 3 years")
        break

Test Case 1

Enter the starting salary: 150000
Best savings rate: 0.4411  
Steps in bisection search: 12 

Test Case 2

Enter the starting salary: 300000
Best savings rate: 0.2206 
Steps in bisection search: 9 

Test Case 3

Enter the starting salary: 10000
It is not possible to pay the down payment in three years

My code passes all test cases but when the input is too high it enters an infinite loop that I don't know how to reconcile.

Answer 1

Essentially when annual salary becomes higher the optimal savings rates becomes smaller. When the optimal savings rate becomes smaller then the level of precision you require for

abs(current_savings - portion_down_payment) <= epsilon

becomes higher. When you cast percent_saved to an int in

percent_saved = int((low + high) / 2.0)

it artificially limits the precision and then code enters an infinite loop.

Remove the cast and the code will work always.