Evaluating lump sums and annuities

Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $61 million, to receive 10 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.5 million.

If she thinks she can earn 7% percent annually, which should she choose?

If she expects to earn 8% annually, which is the best choice?

If she expects to earn 9% annually, which would you recommend?

Explain how interest rates influence the optimal choice.