$$\text{PV} = \frac{\text{FV}}{\left( 1 + r \right)^{n}}$$
$$\text{PV} = \frac{\text{FV}}{\left( 1 + \frac{r}{m} \right)^{n*m}}$$
$$r = \sqrt[n]{\frac{\text{FV}}{\text{PV}}} - 1$$
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rn = rreal + rinf + rrealrinf
$$r_{\text{real}} = \frac{r_{n} - r_{\inf}}{1 + r_{\inf}}$$
$$r_{\text{ef}} = {(1 + \frac{r}{m})}^{m} - 1$$
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$$\text{FV} = R*\frac{{(1 + r)}^{n} - 1}{r}$$
$$\mathbf{R} = \text{FV}*\frac{r}{\left( 1 + r \right)^{n\ } - 1}$$
$$\text{PV} = R*\ \frac{\left( 1 + r \right)^{n\ } - 1}{\left( 1 + r \right)^{n}*r}$$
$$\mathbf{R} = \text{PV}*\ \frac{\left( 1 + r \right)^{n\ }*r}{\left( 1 + r \right)^{n} - 1}$$
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NPV = PV - I
PV = NPV + I
$$\mathbf{\text{NPV}} = \sum_{t = 0}^{n}\frac{\text{CF}_{t}}{\left( 1 + r \right)^{t}} - I_{0}$$
$$\mathbf{\text{PI}} = \frac{\text{PV}}{I_{0}} = \ \frac{\frac{\sum_{}^{}\text{CFt}}{{(1 + r)}^{t}}}{I_{0}}$$
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