Question

Maybe someone can explain why this equation is even used in the bisection method. (balance*(1+(annual interest rate / 12.0))**12.0)/12.0
Correct me if I am wrong but looks like it just returns the amount of balance.

Answer 1

" ... looks like ... " - did you try it?

that equation has nothing to do with bisection algorithm.

it does does have something to do with compound interest
http://en.wikipedia.org/wiki/Compound_interest

that last divide by zero is curious

Answer 2

Oops! Should have been 12.0 not 12/0! You are correct it does have to do with compounding interest but that is the formula suggested to reach the upper bound and a simple balance/12.0 for the lower bound used in bisecting.

Answer 3

you could also use balance itself for the upper bound - it would add a few iterations tho

Answer 4

Professor explained in PDF which contains this problem:
"What is a good upper bound? Imagine that instead of paying monthly, we paid off the entire balance at the end of the year. What we ultimately pay must be greater than what we would’ve paid in monthly installments, because the interest was compounded on the balance we didn’t pay off each month. So a good upper bound would be one-twelfth of the balance, after having its interest compounded monthly for an entire year."

I belive it is quite clear explanation, probably you just missed it.