Need to solve a differential equation word problem.?

Suppose that a state lottery's grand prize is announced to be one million dollars but that actually the winner is paid $ 50,000 each year for the next 20 years. Assuming the state can earn interest on money at an annual rate of 10% (compounded continuously) over those 20 years, how much is the lottery worth in today's dollars? That is, what does it really cost the state today to set aside funds to cover it? Hint: Denoting time in years by t, solve A'= 0.1A - 5000 , A(0)=Ao then set A(20) = 0 and solve for Ao (A sub zero, or A initial). Thank you!