現在価値 (PV)
\begin{align} PV_{Annuity\; Due}&=C \times \left[\frac{1-(1+\frac{r}{n})^{-t}}{\frac{r}{n}}\right]\times(1+\frac{r}{n})\\ PV_{Ordinary\; Annuity}&=C \times \left[\frac{1-(1+\frac{r}{n})^{-t}}{\frac{r}{n}}\right]\\ PV&=\frac {C_{t}}{(1+\frac{r}{n})^{t}} \end{align}
将来的な価値 (FV)
\begin{align} FV_{Annuity\; Due}&=C \times \left[\frac{(1+\frac{r}{n})^{t}-1}{\frac{r}{n}}\right]\times (1+\frac{r}{n})\\ FV_{Ordinary\; Annuity}&=C \times \left[\frac{(1+\frac{r}{n})^{t}-1}{\frac{r}{n}}\right]\\ FV&=C_{0}\times (1+\frac{r}{n})^{t}\\ \end{align}