A company earns 2% per month on its assets, paid continuously, and its expenses are paid out continuously at a rate of $80,000 per month.
(a) Write a differential equation for the value, V, of the company as a function of time, t, in months.
(b) What is the equilibrium solution for the differential equation? What is the significance of this value for the company?
(c) Solve the differential equation found in part (a).
(d) If the company has assets worth $3 million at time t = 0, what are its assets worth one year later?