## A penny saved…

by

In the Futurama episode “A Fishful of Dollars” (Season 1, Episode 6), Fry goes to the bank to check the balance on his old account. The teller explains, “OK, you had a balance of 93¢…and at an average of 2 ¼% interest over a period of 1000 years, that comes to 4.3 billion dollars.”

Question: Was the interest compounded annually, quarterly, or monthly?

Answer: The interest was compounded annually: the exact amount would have been \$0.93·(1.0225)1000 ≈ \$4,283,508,450 or maybe a little more since this incident takes place several episodes after Fry’s 1000-year sleep.

Quarterly compounding would have given Fry \$0.93·(1.005625)4000 ≈ \$5,160,938,941, monthly compounding 5.38 billion dollars, and continuous compounding would have lead to a balance of nearly 5.5 billion dollars.

As a side note, right before going to the bank Fry tried to buy a 3-pack of fancy underwear for \$30, suggesting that inflation had been negligible over the past millennium.

Aside 12/28: On the DVD commentary for this episode, David X. Cohen says about the 4.3 billion dollar figure: “We figured this out three different times on Stuart Burns’ palm pilot.”

The above title screen is from a screenshot of a copyrighted TV show, but according to Wikipedia its use here seems to be fall under U.S. fair use laws because: it is a very low quality screenshot of a TV series title sequence; it does not limit the copyright owner’s rights to sell the TV series in any way; copies could not be used to make illegal copies of the series on another medium; the title sequence image helps to demonstrate its description in this blog entry; and the title sequence does not contain any material from the actual show. And is anyone else amused by the fact that my justification for using the picture is almost as long as the entry itself?