1.Bobby approaches you, and offers you a deal: hell give you $10, 000 today, if you promise to give him the following payment stream: You will pay him $0.01 in exactly one year. Each year after that you will pay him twice what you paid him the previous year. So, in the second year youll pay him $0.02, in the third year youll pay him $0.04, and so on. Notice that these payments get really large, really quickly. For example, after 20 years youre paying about $10, 000!

a) How much money have you paid after n years?

b) Since this is a perpetuity, lets assume that your descendants keep having to pay each year, for the rest of eternity. Pretty grim. Notice that, in the end, youll have ended up paying an infinite amount of money. So, this investment doesnt have a well-defined future value. However, after doing some work, you figure out that if you deposit $5,000 into your bank account now, these savings will be enough to cover this investment. What interest rate does your bank give you? (It will be quite high.)

c) Recall that Bobby is giving you $10,000 right away as payment for this perpetuity. For which interest rates do you make money off this deal?