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Summary: ROOTFINDING
We want to find the numbers x for which
f(x) = 0, with f a given function. Here, we denote
such roots or zeroes by the Greek letter . Rootfind-
ing problems occur in many contexts. Sometimes they
are a direct formulation of some physical situtation;
but more often, they are an intermediate step in solv-
ing a much larger problem.
An example with annuities Suppose you are paying
into an account an amount of Pin per period of time,
for Nin periods of time. The amount you are de-
posited is compounded at at interest rate of r per pe-
riod of time. Then at the beginning of period Nin+1,
you will withdraw an amount of Pout per time period,
for Nout periods. In order that the amount you with-
draw balance that which has been deposited including
interest, what is the needed interest rate? The equa-
tion is
Pin
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