Bisect search using varying hi lo

Question

I am trying to figure out how to use a bisect search to find:

Monthly payment made to clear loan amount

• Monthly interest rate = (Annual interest rate) / 12
• Monthly payment lower bound = Balance / 12
• Monthly payment upper bound = (Balance x (1 + Monthly interest rate)12) / 12

At the moment I have:

balance = 6758
annualInterestRate = 0.20
monthlyRate = annualInterestRate/12
numGuesses = 0
lo = balance/12
hi = (balance)*((1+monthlyRate)**12)/12
monthPay = (hi + lo)/2.0
NuBalance = balance
while abs((NuBalance)*(1+monthlyRate))-(monthPay) >= 0.01:
    print('low = ' + str(lo) + ' high = ' + str(hi) + ' MonthPay = ' + str(monthPay))
    numGuesses += 1
    if ((NuBalance)*(1+monthlyRate))-(monthPay) <= 0.01:
        print('Month Pay LO = ' + str(monthPay))
        lo = monthPay
    else:
        print('Month Pay HI = ' + str(monthPay))
        hi = monthPay
    monthPay = (hi + lo)/2.0
print('numGuesses = ' + str(numGuesses))
print('Month Pay = ' + str(monthPay))

Any help to where I'm going wrong would be appreciated.

Answer 1

It should be:

while abs((NuBalance)*(1+monthlyRate)-(monthPay)) >= 0.01:
                                    ^           ^

and always exists

(hi + lo)/2.0 < (NuBalance)*(1+monthlyRate)

is True because hi and lo both smaller than (NuBalance)*(1+monthlyRate)

In [9]: print 'lo:', lo
lo: 563

In [10]: print 'hi:', hi
hi: 686.720412649

In [11]: print 'monthPay:', monthPay
monthPay: 624.860206325

In [12]: print '(NuBalance)*(1+monthlyRate):', (NuBalance)*(1+monthlyRate)
(NuBalance)*(1+monthlyRate): 6870.63333333