\begin{frame}
  \frametitle{Continuously Compounded Interest}

  \begin{exampleblock}{}
    Assume $1000\$$ are invested with 6\% interest compounded annually.
    \pause Then
    \begin{itemize}
    \pause
      \item after 1 year we have $1000\$ \cdot 1.06 = 1060\$$
    \pause
      \item after 2 year we have $1000\$ \cdot 1.06^2 = 1123.6\$$
    \pause
      \item after $t$ year we have $1000\$ \cdot 1.06^t$
    \end{itemize}
  \end{exampleblock}
  \pause
  
  \begin{block}{}
    If $A_0$ is invested with interest rate $r$, compounded annually, 
    then after $t$ years the amount is
    \begin{talign}
      A_0 \cdot (1+r)^t
    \end{talign}
  \end{block}
  \pause
  
  Usually, interest is compounded more frequently.
  \pause
  
  \begin{block}{}
    If the interest is compounded $n$ times per year,
    then after $t$ years the value is
    \begin{talign}
      A_0 \cdot \left(1+\frac{r}{n}\right)^{nt}
    \end{talign}
  \end{block}
\end{frame}