9. Suppose you win $30 million in the lottery. The state wants to spread the payments out over 20 years, to which you agree for tax reasons. How much will the state have to put into an interest bearing account getting 7% annual interest in order to pay you $1.5 million per year for the next 20 years and have no money left in the account after the end of the 20 years?

This is a depreciating annuity, so you should use the formula for a depreciating annuity

P = R(1 - (1 + r)-n)/r

Since the payments are being made once a year the periodic interest rate is the annual rate and the number of periods is the number of years. This gives us

P = $1,500,000(1 - 1.07-20)/.07

= $15, 891, 021.37

The state has to come up with just over half of the $30 million payout, and nearly half of the money that the state winds up paying out in lottery winnings comes from the interest on that deposit.