Tukukkk

Following is the problem set from MIT opencourseware

Part C: Finding the right amount to save away

1. Your semi­annual raise is .07 (7%)


2. Your investments have an annual return of 0.04 (4%)


3. The down payment is 0.25 (25%) of the cost of the house


4. The cost of the house that you are saving for is $1M.

I am now going to try to find the best rate of savings to achieve a down payment on a $1M house in 36 months. And I want your savings to be within $100 of the required down payment.I am stuck with the bisection search and 'It is not possible to pay the down payment in three years.' this output. I am new to programmers and English.Any help is appreciated.

And here is my code:

starting_salary = float(input("Enter your starting salary:​ "))

months_salary = starting_salary/12

total_cost = 1000000.0

semi_annual_rate = .07

investment_return = 0.04

down_payment = total_cost * 0.25

r = 0.04

current_savings = 0.0

#months = 36

tolerance = 100

steps = 0

high = 1.0

low = 0.0

guess = (high+low)/2.0

total_salaries = 0.0

def calSavings(current_savings,months_salary,guess,month):

    for months in range(0,37):

        if  months%6==1 and months >1:

            months_salary=months_salary*(1+semi_annual_rate)

        current_savings = current_savings + months_salary * guess

        current_savings = current_savings * (1+0.04/12)

    return(current_savings)

current_savings = calSavings(current_savings,months_salary,guess,1)

while abs(current_savings-down_payment)>=100:

    if  current_savings < down_payment:

        low = guess

    elif current_savings > down_payment:

        high = guess

    else:

        print("It is not possible to pay the down payment in three years.")

        break

    guess = (low+high)/2

    steps = steps +1

print("Best saving rate: ", guess)

When I run this code, it will be stuck. I don't know why.
And I don't know how to determine which is the condition of output this "It is not possible to pay the down payment in three years."

I have seen Similar questions on stackoverflow like this and this but I am not quite followed.

I've already addressed most of my points in the comments, but I will recap:
You are trying to solve a problem using a method called recursive solving, in this case using the bisection method.

The steps are as follows:

1. start with an initial guess you chose 0.5
   


2. Perform your calculations in a loop and iterate the initial guess, in this case you must account for the following:


3. Maximum number of steps before failure, remember we can always add 2 values and divide by 2, your result will tend to 0.999999.. otherwise


4. A certain tolerance, if your step size is not small enough 25% of 1 M is 250 000 and you might never hit that number exactly, that' why you make a tolerance interval, for example: anything between 250 000 and 251 000 --> break loop, show result.


5. Your if statements for changing low and high to adjust guess are correct, but you forget to re-initialize savings to 0 which means savings was going to infinity.

Now that's all said, here's a working version of your code:

starting_salary = 100000  # Assuming Annual Salary of 100k 

months_salary = starting_salary/12

total_cost = 1000000.0

semi_annual_rate = .07

investment_return = 0.04

down_payment = total_cost * 0.25

print("down payment: ", down_payment)

r = 0.04

current_savings = 0.0

#months = 36

tolerance = 100

steps = 0

high = 1.0

low = 0.0

guess = (high+low)/2.0

total_salaries = 0.0

tolerance = down_payment/100 # I chose this tolerance to say if my savings are between [down_payment - (downpayment + down_payment/100)]  result is admissible. (this is quite a high tolerance but you can change at leisure)

def calSavings(current_savings,months_salary,guess,month):

    for months in range(0,37):

        if  months%6==1 and months >1:

            months_salary=months_salary*(1+semi_annual_rate)

        current_savings = current_savings + months_salary * guess

    current_savings = current_savings * (1+0.04)

    return(current_savings)



while abs(current_savings-down_payment)>=100:

    current_savings = calSavings(current_savings,months_salary,guess,1)

    if  current_savings < down_payment:

        low = guess

        current_savings = 0.

    elif current_savings > down_payment + tolerance:

        high = guess

        current_savings = 0.

    if (steps > 100): # I chose a maximum step number of 100 because my tolerance is high

        print("It is not possible to pay the down payment in three years.")

        break

    guess = (low+high)/2

    steps = steps +1



print("Best saving rate: ", guess)

print("With current savings: ", current_savings)

Output:

down payment:  250000.0

Best saving rate:  0.656982421875

With current savings:  250072.3339667072

[Finished in 0.08s]