Question:

Fatima invests $\displaystyle \$100$ per month for a complete year, with interest added every month at the rate of $\displaystyle \frac{1}{2}\%$ per month at the end of the month. How much would she have had to invest at the beginning of the year to have the same total amount after the complete year?

Attempt:

$\displaystyle \frac{100(1-1.005^{12})}{(1-1.005)} = \$1233.56$

Don't know what to do next!