[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][/tex]
[tex]\begin{cases} A= \begin{array}{llll} \textit{accumulated amount}\\ \end{array}\\ pymnt=\textit{periodic payments}\dotfill &\$5618\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A=5618\left[ \cfrac{\left( 1+\frac{0.10}{2} \right)^{2\cdot 4}-1}{\frac{0.10}{2}} \right]\implies A=5618\left( \cfrac{1.05^8~~ - ~~1}{0.05} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 53646.89~\hfill[/tex]
