Question

I'm having some trouble with Problem Set 1, Part 3. The first two parts were easy, but I'm a little confused on how to implement bisection searching. I understand the concept well, but not sure what conditional to use to know when I've found the minimum monthly payment (mmp).

I have looked at a few different examples and tested them, but I am getting incorrect answers. I thought perhaps the problem was that the floats were not limited to two decimal places, but adding round() to the upper and lower bounds seems to result in an infinite loop.

Using an example from http://stackoverflow.com/questions/12820003/bisection-search?rq=1

Answer 1

This is my output:

Enter the outstanding balance on your credit card: 320000
Enter the annual interest rate as a decimal: .2

RESULT
Monthly payment to pay off debt in 1 year: $26666.6673641
Number of months needed: 11.9999996862

Answer 2

I used:
if balance <= 5 and balance > 0:
print "**if"
print "Your minimum payment is:", guess
print balance
break
elif balance > 0:
print "**elif, balance is to high, guess being tested was to low"
print "current lowerGuess", lowerGuess
print "current guess", guess
lowerGuess = guess
print "new lowerGuess", lowerGuess
guess = (higherGuess + lowerGuess)/2
print "new guess", guess
else:
print "**else, balance was to low, guess being tested was to high"
print "current higherGuess", higherGuess
print "current guess", guess
higherGuess = guess
print "new higherGuess", higherGuess
guess = (higherGuess + lowerGuess)/2.0
print "new guess", guess

and it seems to be working. the print statements are just in there to show me what's happening. it basically says that getting the balance down to $5 or less is good enough.

Answer 3

is it in Python? @kpennington89

Answer 4

Yes.

I am getting closer. I did realize an error I didn't notice before: I was using the wrong equation to calculate remaining balance.

The assignment is to find the minimum monthly payment to the nearest cent, so I would prefer to do that than to the nearest $5.

Here is my code at the moment:
while mmp*12 - bal >= 0.01:
remain = bal
for month in range(0,12):
remain = round(remain * (1+monthly) - mmp,2)
#print "\nmonth: " + str(month+1)
#print "remaining balance: " + str(remain)

if remain < -0.2:
#guess too high
upper = mmp
mmp = round((lower+upper)/2,2)
print "\nremaining balance: " + str(remain)
print "mmp = " + str(mmp)
print "lower: " + str(lower)
print "upper: " + str(upper)
elif remain > 0.01:
#guess too low
lower = mmp
mmp = round((lower+upper)/2.0,2)
print "\nremaining balance: " + str(remain)
print "mmp = " + str(mmp)
print "lower: " + str(lower)
print "upper: " + str(upper)
else:
break

print "\nRESULT\nMonthly payment to pay off debt in 1 year: $" + str(mmp)
print "Number of months needed: " + str(round(bal/mmp,2))


Which results in an accurate answer for the first test case:

Enter the outstanding balance on your credit card: 320000
Enter the annual interest rate as a decimal: .2
RESULT
Monthly payment to pay off debt in 1 year: $29643.05
Number of months needed: 10.8

BUT the result for the second test case is off by $0.01. Caused by using round()? :

Enter the outstanding balance on your credit card: 999999
Enter the annual interest rate as a decimal: .18
RESULT
Monthly payment to pay off debt in 1 year: $91679.9
Number of months needed: 10.91


I also noticed that in his handout the # of months required is not accurate for the minimum monthly payment in his results. It says 12 for both when really it rounds up to 11 months. I suppose these results are good enough! Thanks all for your help!