A young person with no initial capital invests $k$ dollars per year in a retirement account at an annual rate of return $0.04$. Assume that investments are made continuously and that the return is compounded continuously.

a) Write a differential equation which models the rate of the change of the sum $S(t)$ with $t$ in years (this will involve the parameter $k$).
$S' =$
Note: Use $S$ rather than $S(t)$ since the latter confuses the computer.

b) Use part a) to determine a formula for the sum $S(t)$ -- (this will involve the parameter $k$):
$S(t) =$

c) What value of $k$ will provide $1661000$ dollars in $48$ years?
$k =$