How can you invest the one time payout to match the yield of the lottery's annual annuity? (See details)

If you win one of the big lotteries such as the Mega-Millions (recently hit $319 million) or Powerball (currently at $153 million) you have a choice of taking a one time payout at about 50% of the stated jackpot, or collecting the full amount over a series of years. For instance, if you won the $153 million Powerball jackpot and opted for the one time payout, you would receive $77.4 million before taxes. If you went for the annuity, you would get 30 annual payments of $5.1 million each before taxes. The Mega Millions works in a similar fashion, but has a 26 year annuity, so annual payout for the same prize size are slightly higher with it, and the one time payout is less than 50%. In each case, the actual jackpot is what you get in a one-time payout. If you elect the annuity, the lottery invests the real jackpot money in investment instruments that yield enough to provide the larger payout over time even though annual withdrawals are being made from the principal invested.

Say you win a big jackpot like the current Powerball $153 million and you aren’t certain that the lottery’s investment holders will remain solvent for 30 years and actually pay out your full winnings. Therefore, you elect to cut the winnings in half and take it in a lump sum. How could you invest the bulk of that lump sum so that it would be reasonably safe and would end up paying you as much, or nearly as much, as the lottery had promised in the sanitized prize?