Suppose a friend of yours invests $$100$ each month in an individual retirement account $($IRA$)$ for a decade

and earns an unbelievable APR of $12\%$ a year $(1\%$ per month$)$ on her investment. She will end up with $$100($F$/$A$,1\%,120)=$ $$100(230\mathrm{.}0387)=$ $$23,003\mathrm{.}87$ after $10$ years. If you decide to invest $$200$ each month over $10$ years, but can earn only a meager APR of $3\%$ per year on it$,$ roughly how much will you have accumulated after $10$ years?