You are a wealthy individual who has money to invest. You decide to make a one-time investment in a hedge fund with the goal that in 10 years your investment will be worth exactly one million dollars.
The hedge fund promises a 10 percent annual return, and it charges a flat fee of $15,000 per year to participate.
Write down the differential equation governing your investment, y(t), in dollars, at time t > 0, in years, for an arbitrary initial value of y_0 at time t = 0.
Determine the (minimum) initial investment y0 that will achieve your goal.
[Assume continuous compounding of returns and continuous payment of the fee.]