Models & Qualitative Behavior · Challenge problem

An endowment earns interest compounded continuously at $5\%$ per year and pays out continuously, starting at $1000$ dollars per year and rising with inflation at $3\%$ per year, so its balance obeys $B' = 0.05B - 1000e^{0.03t}$. What is the smallest starting balance $B(0)$ for which the endowment never runs out of money?