A young person with no initial capital invests $k$ dollars per year in a retirement account at an annual rate of return $0.06$. Assume that investments are made continuously and that the return is compounded continuously.

Determine a formula for the sum $S(t)$ -- (this will involve the parameter $k$):
$S(t) =$

What value of $k$ will provide $2513000$ dollars in $50$ years?
$k =$