A lottery offers two options for a prize, A and B, as shown below. 

Option A: $1,000 a week for life.

 Option B: $1,000,000 in one lump sum.

If you choose Option B, you have the opportunity to place the winnings into an investment that also makes regular payments, at a rate of 3%/a, compounded weekly. The annuity will pay out a specific amount weekly based on how long you want the annuity to last.

1. Which option would the winner choose if you expect to live for another:
   • 20 years?
   • 50 years?
2. Use technology to determine the range of life expectancies when each option is preferred. Show your work.