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

a$.$ Which option would the winner choose if you expect to live for another:

$20$ years?

$50$ years?

b$.$ Use technology to determine the range of life expectancies when each option is preferred. Show your work.

c$.$ Write a brief reflection about which option you would choose, and why.

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.