INVESTMENT: Let A be the amount in a fund earning interest at the annual rate of r, compounded continuously. If the continuous cash flow of P dollars per year is withdrawn from the fund, then the rate of decrease of A is given by the differential equation:
dA/dt = rA - P
where A = A_0, when t = 0
a) solve this function for A as a function of t
b) use the result of part (a) to find A when A_0 = $2,000,000, r = 7%, P = $250,000, and t = 5 years
c) find A; if a retired person wants a continuous cash flow of $40,000 per year for 20 years. Assume that the person's investment will earn 8%, compounded continuously.
This provides an example of working with differential equations and compound interest.