Question: A bank account earns 5% annual interest compounded continuously. Continuous payments are made out of the account at a rate of $12,000 per year for 20 years.
(a) Write a differential equation describing the balance B = f(t), where t is in years.
(b) Solve the differential equation given an initial balance of B0.
(c) What should the initial balance be such that the account has zero balance after precisely 20 years?