he's 24 right now, and retiring at 65 means 41 years later.
[tex]\bf ~~~~~~~~~~~~\textit{Future Value of an annuity due}\\
~~~~~~~~~~~~(\textit{payments at the beginning of the period})
\\\\
A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)
\\\\
[/tex]
[tex]\bf \qquad
\begin{cases}
A=
\begin{array}{llll}
\textit{accumulated amount}\\
\end{array}
\\
pmt=\textit{periodic payments}\to &200\\
r=rate\to 2.95\%\to \frac{2.95}{100}\to &0.0295\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{they're done monthly, thus}
\end{array}\to &12\\
t=years\to &41
\end{cases}[/tex]
[tex]\bf A=200\left[ \cfrac{\left( 1+\frac{0.0295}{12} \right)^{12\cdot 41}-1}{\frac{0.0295}{12}} \right]\left(1+\frac{0.0295}{12}\right)
\\\\\\
A=200\left[ \cfrac{\left( 1 +\frac{59}{24000}\right)^{492}-1}{\frac{59}{24000}}\right]\left(1+\frac{59}{24000}\right)
\\\\\\
A=200\left[ \cfrac{\left( \frac{24059}{24000}\right)^{492}-1}{\frac{59}{24000}}\right]\left(\frac{24059}{24000}\right)\\\\\\A\approx 191398.48860411668565454023[/tex]
