[tex]~~~~~~~~~~~~\underset{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}}\\ \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount} \\ pymnt=\textit{periodic payments}\dotfill &\$5000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]A=5000\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1\cdot 12}-1}{\frac{0.04}{1}} \right]\implies A=5000\left( \cfrac{1.04^{12}~~ - ~~1}{0.04} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 75129.03~\hfill[/tex]
