Jacinda is $30$ years old and intends to retire at age $65.$ According to the estimation of life expectancy for Canadian women, they expect to live for $25$ years into retirement, and therefore needs to save enough funds in the next $35$ years to support herself for another $25$ years after retirement. She plans to make monthly contributions to a mutual fund earning $12\mathrm{.}0\%$ annually, and then at retirement, will put her savings into guaranteed investment certificates $($GIC$$s$),$ paying $4\mathrm{.}0\%.$ Taking inflation into account, Karen estimates that she will need a monthly income of $$4000$ throughout retirement. How much must she invest each month in the mutual fund to ensure this standard of living? Assume that there is monthly compounding for the mutual fund.