MIT- 6.00.1x || week 2 || pset-2 || problem-3

problem- 3

annualInterestRate = 0.2
balance = 320000


# variable for Monthly Interest rate
mir = annualInterestRate / 12.0
pb = balance

#lower bound
lwb = balance /12

#upper bound
upb = (balance*((1+mir)**12))/12.0

#middle bound
mmp = (lwb+upb)/2

# test function
def test():
    # minimum monthly payment
    global mmp
    mmp = (lwb+upb)/2

    global pb
    pb = balance
    
    for n in range(12):
        # monthly unpaid balance
        mup = pb - mmp
        pb = mup + (mup * mir)
    

while True:
    if pb <= 0 and abs(pb) < mmp:
        break
    elif pb < mmp:
        lwb = mmp
        test()
    elif pb > mmp:
        upb = mmp
        test()
    

print("Lowest Payment: " + str(round(mmp, 2)))