The Real Value of the Lottery You must be careful about money. Lottery winners sometimes think they are millionaires when they’re not really as rich as they think. Furthermore, there are enormous income taxes to be paid. But in these problems we are just calculating pretax earnings. 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 10% 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′ = 0.10A − 50,000, A(0) = A0; then set A(20) = 0 and solve for A0.
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