The amount of money in an account, S(t), which starts with $S0 and grows with a continuous annual interest rate of r and continuous deposits of $D per year can be modelled by the initial value problem:
dS/dt = r.S+D, s(0)=S0
Suppose that two students after graduation, open Retirement accounts at age 21. Both students earn a continuous annual interest rate of 8% on their investments. Student A inherits $1, 000, 000, which they put into their retirement account when they open it and then makes no additional deposits before they retire at age 75. Student B start with $0 balance in their account when they open it, but makes continuous yearly contributions of $D per year.
Find the amount D that Student B needs to make in yearly contributions to retire with the same amount of money as Student A at age 75.