We hypotize the 'cash flow' of the Central Bank is constant, so that each day $50 milions come in and $50 milions go out, and $50 milions are the entire circulating capital multiplied by .005. Now we set...

(1)

The DE for is...

, (2)

... where tha variables are separable. The solution is...

(3)

With the 'initial condition' is so that is...

(4)

It will be at the time ...

Kind regards