Pennies for Mowing the Lawn

Spring has finally arrived, and li’l Timmy wants to make some money mowing lawns. He approaches his elderly neighbor, Gramps Poppy, offering to mow his lawn regularly until winter comes again. Gramps says “How about I pay you $10 to mow my lawn each week for the next thirty weeks? That’s $300!”

But Timmy retorts, “Nah bro, how about this: I’ll mow your lawn for thirty weeks, sure, but you only need to pay me in pennies. The first week it’s just 1¢, then the next week you pay me 2¢, then the next week it’s 4¢, then 8¢, and so on, doubling the number of pennies each week. How about that?”

It sounds like such a good deal! Poppy thinks, and accepts the offer after no thought at all.

How much money is li’l Timmy projected to make on the last day he mows Gramp Poppy’s lawn?