$1.$ You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $$200,000$ today or receive payments of $$1,500$ a month for $20$ years. You can earn a $8\%$ annual rate on your money, compounded monthly. Which option should you take and why?

A$.$ You should accept the $$200,000$ lump sum because the monthly payments are only worth $$195,413$ to you today.

b$.$ You should accept the $$200,000$ lump sum because the monthly payments are only worth $$178,799$ to you today.

c$.$ You should accept the monthly payments because they are worth $$215,844$ to you.

d$.$ You should accept the monthly payments because they are worth $$209,371$ to you.

e$.$ You should accept the $$200,000$ lump sum because the monthly payments are only worth $$17,799$ to you today.