Laura has decided that she wants to build enough retirement wealth that, if invested at $6\mathrm{.}50\%$ per year $($compounded monthly$),$ will provide her with $$3,500$ of monthly income for $25$ years. To date,she has saved nothing, but she still has $30$ years until she retires. How much money does Laura need to contribute per month to reach her goal?

$$468\mathrm{.}60$

$$536\mathrm{.}90$

$$415\mathrm{.}65$

$$573\mathrm{.}10$

$$390\mathrm{.}86$