Karen Kushida is $25$ years old, and intends to retire at age $65.$ According to the estimation of life expectancy for Canadian women, she expects to live for $20$ years in retirement. Therefore, Karen needs to save sufficient funds in the next $40$ years to provide for herself for the subsequent $20$ years. She plans to make monthly contributions to an equity$-$based mutual fund earning $10\mathrm{.}5\%$ annually. At retirement, Karen will put her savings into guaranteed investment certificates $($GIC$$s$),$ paying $5\mathrm{.}5\%.$ Taking Canada Pension Plan income as well as inflation into account, Karen estimates that she will need a monthly income of $$4000$ throughout retirement. How much must she invest each month in mutual fund to ensure this standard of living? Assume that there is monthly compounding for the mutual fund. $*($I need to use the formula FV$=$C$(1+$r$)^$t$-1/$r$)$