#!/usr/bin/python

def amort(cost, interest, term, pmt):
    mint = (1 + interest) ** (1.0/12)
    for i in range(term):
        for j in range(12):
            cost *= mint
            cost -= pmt
    return cost

def findpmt(cost, interest, term):
    ub = cost
    lb = 0
    test = cost / 2
    bal = amort(cost, interest, term, test)
    while abs(bal) > 1000:
        if bal > 0:
            lb = test
        else:
            ub = test
        test = (lb + ub)/2
        bal = amort(cost, interest, term, test)
    return test

def ira(down, pmt, interest, term):
    mint = (1 + interest) ** (1.0/12)
    for i in range(term):
        for j in range(12):
            down += pmt
            down *= mint
    return down