Originally Posted by

**jonah** You must have meant:

for any

$\displaystyle \left\{ \begin{array}{l} c < m \\ c = m \\ c > m \\ \end{array} \right.

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If so, then

$\displaystyle S = R \cdot \frac{{\left( {1 + {\textstyle{r \over c}}} \right)^{yc} - 1}}{{\left( {1 + {\textstyle{r \over c}}} \right)^{{\textstyle{c \over m}}} - 1}} = 4,000\frac{{\left( {1 + {\textstyle{{.08} \over 4}}} \right)^{10 \times 4} - 1}}{{\left( {1 + {\textstyle{{.08} \over 4}}} \right)^{{\textstyle{4 \over 2}}} - 1}} \approx \$ 119,607.8875...

$

If $\displaystyle c \to \infty$, then

$\displaystyle S = R \cdot \frac{{e^{ry} - 1}}{{e^{{\textstyle{r \over m}}} - 1}}$