[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 &150\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &35 \end{cases}[/tex]
[tex]A=150\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12\cdot 35}-1} {\frac{0.04}{12}} \right]\implies A= 150\left[ \cfrac{\left( \frac{301}{300} \right)^{420}~~ - ~~1}{\frac{1}{300}} \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill A\approx 137059.64~\hfill[/tex]
