At the beginning of every year a bank customer deposits v euros in an investment fund and withdraws, at the end of the n-th year, a capital of M euros. We want to compute the average yearly rate of interest r of this investment. Since M is related to r by the relation
$M = v\sum_{k=1}^n[(1 + r)^k] = v[(1 + r)/r][(1 + r)^n − 1]$ , we deduce that r is the root of the algebraic non-linear equation:
$f(r) = 0$, where $f(r) = M − v[(1+r)/r][(1 + r)^n − 1]$.
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