Alottery offers two options for the prize.

option a: $1000 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.

a. which option would the winner choose if you expect to live for another:
i. 20 years?
ii. 50 years?
b. use technology to determine the range of life expectancies when each option is preferred. show your work.