It's the simplest way to turn time into money: drop a few dollars into a compound interest bank account, then hop into your Time-O-Matic or become Cryogenically Frozen and come back in a couple dozen decades to find that your pocket change has exponentially increased to a fairly tidy fortune.
Of course, this particular moneymaking scheme is dependant on a few variables remaining constant at both ends of your time journey. The first being that no world-spanning disaster occurs and renders all forms of money worthless. The second being that Ridiculous Future Inflation doesn't counteract the effects of compound interest, meaning that you only get slightly richer at the end. The third being that the financial institution in which your dollars are stored never becomes bankrupt or closes in the intervening years. The fourth being that, in your prolonged absence from reality, your assets aren't seized under laws of escheatment. And, of course, that said financial institution doesn't have a 'no time travelers' policy to prevent this kind of scheme from occuring. Lastly, there are professional embezzlers in every generation, and an untouched, forgotten account that's been around longer than a human can live would present a mighty tempting target.
A more secure way would be to invest in something that regularly outpaces inflation (like stocks or bonds). The best way (especially if you can control the time travelling), is to make numerous stops, investing in securities that have very high short-term returns (for example, a stock that jumps 20% in value in one day, but overall has average growth), and continually reinvesting the returns. This removes most of the problems above, but may get you arrested for insider trading.
Another variable that is rarely mentioned in fiction is the need for authentic-period currency. A dollar bill will obviously get you nowhere in Feudal Japan, but the more detailed design on a series 2004 $20 bill is likely to be considered counterfeit anytime before 2004 (depending on how much the other party is paying attention, but bank tellers would be the most likely people to spot that kind of thing; oh, and don't forget that most coins have the year they were made on them.). You do not, however, have to go that far back in time. Just grab what's in your pocket, remove everything printed in the last year, travel to one year ago, and invest that. You wouldn't get your money in your present, but you may get it in the way cooler than your present future.
The reverse is much easier, though; a 1928 $500 or $1000 bill is still legal tender, although worth much more than its face value to collectors. This of course raises the possibility of gathering collectibles before the majority are destroyed or lost, but that opens a whole new can of worms in terms of authentication and ensuring your actions don't eliminate its future worth, not to mention you ought to leave the currency in a safe place then travel back separate from it and retrieve it - trying to sell a 1928 bill in 2012 that has not obviously aged 84 years will make collectors suspect the bill is counterfeit, even though it isn't. The bill will seem too new. Alternatively, a prospective time-traveler could get around the currency problem by using their seed money to purchase non-currency valuables, like jewels or precious metals, and then sell those at your investment-point to get chronologically appropriate tender. But watch out that they aren't Worthless Yellow Rocks in the future.
And of course, if any of these tactics are indeed possible, you probably won't be the only one to notice this. Hordes of time-travelers attempting to manipulate currency is sure to result in the eventual destruction of the economy. Time-travel responsibly, folks.
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Anime and Manga
In Doraemon, Nobita has Doraemon do this in an attempt to get a better allowance; though he does earn a buttload of interest, the bills are in future currency, so it only nets him a modest increase when it gets exchanged for present day bills.
In a Tenchi Muyo! 4koma, Kiyone Makibi attempts to do this after the time traveling adventures of The Movie.
Mystery in Space #12 "The Richest Man on 9 Planets". Sam Drake invents a suspended animation drug. After bank-deposting the single dollar he has left after paying his bills, he goes to sleep for a thousand years. Waking up in his miraculously still-intact basement in clothes that are still in perfect condition, he goes to the bank and retrieves his now $250,000 balance. Worried about changing monetary values, Sam tells the bank manager to invest his money in gold and goes to sleep for another thousand years, only to wake up in a world where gold is now common due to a cosmic accident.
There's a variation in a recent Spirou and Fantasio story where the villain goes back to the nineteenth century to buy houses in the Marais quarter in Paris, then a common slum, now the most expensive part of the city.
Léonard le Génie tries the invest-wait a day-go back trick once, but gets arrested for insider trading.
A Disney comic had the Beagle Brothers (and their mom) travel back in time to take advantage of how much cheaper everything was then... and paying with present-day money. Naturally they get caught and accused of forgery, as all their bills have wrong yearmarks.
Another Disney comic has Donald Duck trying something similar. Scrooge tells him that he bought all properties in Duckburg and thus now owns most of the city. Before he can finish his story Donald gets an idea and runs away. Donald then buys old money from collectors, is sent into past by Gyro and buys all properties before Scrooge does so. He then returns back to the future, but instead of him being the owner of town, Scrooge still rules. Donald goes back to his uncle and asks him to tell the whole story. Scrooge says that someone had bought all properties, but then disappeared. So when the properties fell under compulsory auction to cover unpaid taxes Scrooge bought them all.
A comic story had Pinky and the Brain planning to use a time machine to exploit the trope. They'd open a savings account in present time and then go to the future to collect their winnings. Their first obstacle was finding a bank that agreed to start a savings account with 37 cents. After they finally found one and opened their account, the bank was robbed and they went back in time to prevent their past selves from leaving their money there in the first place. Brain's worries about Never the Selves Shall Meet was justified as somehow it changed the world to have it ruled by ''ostriches''.
MAD made fun of the naive interest idea with a three-frame comic where an early-20th century father gives his son $10,000 and admonishes him to put it in the bank (as opposed to the son's idea of frivolously buying a new car), the son passing on the money (now $67,000) to his son with the same admonition, and the grandson passing on a full $100,000 to his son. The great-grandson remarks that a hundred grand is roughly the same money as ten was in his granddad's day... whereas if granddad had bought a Rolls Royce like he wanted, he'd now have an antique car worth $250,000.
This is invoked by Idiocracy's Joe to convince Frito to lead him to the time machine. Frito doesn't quite understand how it works, so he thinks he'll get the money even if he leads Joe to a fake "time machine" that's actually an amusement park ride.
Time Cop has time villains trying to buy Wall Street stock on the day of the 1929 crash, and cheap Hollywood land back when it was only worth a few cents an acre.
A scene in Back to the Future II strongly implies Doc Brown engages in this. Marty needs some money from the timeline they're in, and Doc opens a briefcase with neatly arranged stacks of bills of various colors and sizes.
All you have to do is deposit one penny in a savings account in your own era, and when you arrive at the End of Time the operation of compound interest means that the fabulous cost of your meal has been paid for. This, many claim, is not merely impossible but clearly insane...
In Life, the Universe and Everything, this is also how Wowbagger the Infinitely Prolonged makes money, by investing in long-term stocks and generally outliving the hell out of everybody.
In "John Jones's Dollar" by Harry Stephen Keeler, a man deposits a dollar in a bank, stipulating that it and its accumulated interest are to be paid to "no other person than [his] fortieth descendant ... along the oldest child of each of the generations which would constitute his posterity". By the time the fortieth generation rolls around, the payout is greater than the total value of the combined holdings of the entire human race. And then the 39th descendant dies childless, with the result that nobody owns anything, and humanity is forced to become a communist utopia. Which is of course absurd on multiple counts, but then this is Harry Stephen Keeler. The most obvious reason why this plan wouldn't work is that, since the 39th descendant died without issue, the Will of John Jones cannot be carried out and so his property would be considered intestate (no will that can be carried out), and all his assets would be absorbed into the State Treasury.
In H. G. Wells's When the Sleeper Wakes the protagonist, after sleeping for 200 years, wakes to find his fortune has accumulated to the point where he owns more than half the world. The trustees of his estate are the world's rulers. He becomes the figurehead for an opposition party that wants to take control, but once they have, realises they're no better than the first lot. Despite his wealth there isn't a lot he can do to make things better, since he's just one man and doesn't understand the world around him very well.
Mentioned (thus becoming an Ur Example) by a friend of the Time Traveler in The Time Machine. The Writer shoots this idea down by pointing out that the investor might arrive to find that the future society has gone communist and abolished money.
The Sleeper's funds weren't all just interest. If I recall correctly, it was stated that one of the Sleeper's relatives as well as the man he fell asleep at became financially successful, and both chose to have the Sleeper inherit them. (The trustees of the estate are also protrayed as extremely aggressive businessmen, and the Sleeper's wealth owes at least as much to their finaglings as to the effects of compound interest.)
The German novel Eine Billion Dollar (that's a trillion dollars in English), by Andreas Eschbach, has this trope as a premise: John Fontanelli inherits the fortune, originally just 300 florins, which his ancestor in the 16th century left for him. Along with the prophecy that the heir will give mankind its lost future back.
In "The Price of Oranges", a short story by Nancy Kress, an elderly man discovers a time corridor, and uses it to bring back fine cigars and fur coats bought 'cheaply' in 1937. It never occurs to him to buy gold certificates which will be worth a fortune now, but as the story shows he's well-meaning, but not very bright.
Subverted by another Heinlein novel, The Door into Summer where the protagonist is put into cold sleep for 30 years and wakes up penniless due to the company managing his finances having gone bankrupt. The second time he cold sleeps, after having gone 30 years back into the past, he arranges for a better financial adviser and awakes to significant profits.
In the Hyperion Cantos by Dan Simmons it's mentioned that one character (Martin Silenus) was put in suspended animation by his parents to pay off the family debt. He wakes up to find that all the accounts and debts have been frozen and then dissolved into the galactic economy, and he has to work as a common laborer.
Averted by the rich villain's plan in The Anubis Gates by Tim Powers. Scheming to travel into the past and invest his wealth there, he also intends to become immortal and watch over his investment, taking full advantage of his economic foresight, rather than trust in compound interest alone.
In the Ender’s Gameuniverse, Andrew "Ender" Wiggins gains quite a bit of money by moving from star system to star system at relativistic speeds. After some careful managing and over a thousand years of travel his account is sufficient to buy a planet. It should be noted that the only reason it works for Ender (and his sister Valentine) is that he has a sentient AI operating in real time keeping track of his investments. His money isn't just sitting in an account gathering interest, it's actively and intelligently being invested even while he's in relativistic travel.
In The Belgariad, Polgara does this the old-fashioned way. She puts a trustworthy person in charge of investing the token rents for land in her former duchy ... and then lives a couple thousand years. By this point, she could probably buy herself a kingdom if she felt like it, and may be one of the richest if not the richest person in the world. Too bad she has absolutely no interest in money. This may also not be an example, because the money isn't invested; it's simply the accumulation of small rents over the course of millennia. Her case is also aided by a severe case of Medieval Stasis and the fact that the tense relations with the Angarak nations prevent their massive deposits of red-gold playing a part in the Western economy.
Used by interstellar travelers in Stephen Baxter's Manifold: Space, who are frozen in time while traveling through the portal network. It works at first, but laws are eventually passed and assets seized, leaving the travelers flat broke when they return.
Vernor Vinge's Marooned In Realtime begins with a 'colony' consisting of all the people that were in stasis during the 'singularity' that saw everyone else on Earth vanish in some unknown way. A pair of brothers are two of the travellers who were in stasis attempting just such a plan.
Clifford Simak's Why Call them Back From Heaven? is a variation: "Give us all your money, and we'll resurrect you in distant future when we'll invent time-travelling". That means "never", because time-travelling is proved impossible.
Another story plays the "anabiosis + interest money" scheme completely straight.
In The Dark Tower series, Eddie comes up with a plan to outmaneuver the Sombra Corporation's plot against the rose, by investing Odetta's capital from Holmes Dental in Microsoft and other up-and-coming businesses in 1977. Given such financial guidance, he predicts their Tet Corporation will one day be able to buy North Central Positronics out from under the bad guys by cashing in the investments in 1987.
Subverted in The Forever War, and hard. The soldiers get quadruple pay for being away in space in a combat zone for the equivalent of twenty years. But by the time the soldiers get back to Earth from their first tour of duty, their money is worthless due to hyperinflation and chronic shortages caused by the war and a world-wide famine. And the size of their compounded pay puts them in a 92% tax bracket. At the end of the novel, most other humans are clones who do not use money, so all of their combat pay is worthless. At one point, William, the narrator, buys a hugely expensive bottle of ancient French brandy to share with his officers, reasoning that investing the money was the alternative. note Elsewhere, there are still colonies where people are normal, and presumably still use money.
It's given an offhand mention in The Dresden Files a couple times. But it's never just sitting around collecting interest, as the White Council has several staff members (pun not intended) that are tasked with managing the Council's finances.
Also part of the reason why Madeline Raith doesn't firebomb Harry's house looking for Morgan, as she doesn't realize that Harry hasn't had a chance to shore up his accounts yet. Also, she's just a Rich Bitch that's Rich in Dollars, Poor in Sense.
In Tom Holt's Flying Dutch, the legendary Flying Dutchman had a life insurance policy which still paid off several centuries later-so much so that to cash it in would bankrupt the entire world economy,
In Compounded Interest, a 1956 short story by Mack Reynolds a time traveler places a small sum at 10% in a bank in medieval Venice and renews the contract every 100 years. By 1960s the sum exceeds the price of everything in the world several times over. Then he comes to the organization servicing The Contract and starts gradually withdrawing money. What for? To build a time machine to go to medieval Venice to place the money. You see, when The Contract employees concluded the scheme was started by a time traveler, they consulted with several famous physicists, including him, about the possibility of time travel. He told them time travel was impossible, but later figured that it was possible, only R&D would be prohibitively expensive. Thus he came with the plan and started withdrawing money before he deposited anything.
In David Weber's Honor Harrington series, this was the plan of the founder of Manticore. After his investment group bought the rights to the planet and system, he put what was left into a trust. Since this was prior to the invention of FTL travel, the colonists had to be Cryogenically Frozen, and travel on a Sleeper Ship. When the colonists finally arrived and were unfrozen around six hundred years later, the trust had grown considerably.
A non-time-traveler example in The Lost Fleet. At the end of the main series, Captain John Geary, who has spent the last 100 years as a Human Popsicle, has finally returned the titular fleet to The Alliance space. He plans to take some R&R. His former lover Victoria Rione tells him that, with his accumulated pay, he should be pretty well off. Geary informs her that the fleet bureaucracy has determined that survival sleep did not count being on duty, specifically to avoid paying officers and sailors for the possible years and decades spent on ice; therefore, his pay was suspended when he was declared MIA. His accounts were frozen as well. Thus, the only pay he has now is only from the moment he was awakened. Luckily, the same rules don't apply to seniority, otherwise he would've never been given command of the fleet.
Another unlucky Human Popsicle in Larry Niven's A World Out of Time found out the hard way that the courts of his time ruled those like him could not own property and thus the assets he set up for himself were long gone. An organization referring to themselves as "The State" transferred the memories of "corpsicles" into mindwiped criminals to do jobs that "citizens" refused to do.
The titular character of Angel is notable for not attempting this. Many vampires and demons use their long lifespans and considerable powers to form and maintain successful businesses. By contrast, Angel has to charge the people he helps because, as Cordelia points out, he never bothered to make any investments over a 200 year life. Apparently when he was the evil vampire Angelus, if he wanted something he'd just kill the owner and take it, a pattern of behaviour that doesn't encourage a creature of the night to put aside for a sunny day.
In the Doctor Who serial The Time Meddler, the eponymous meddler claims to have done this. Though given what had already been shown in previous serials, he would have had to withdraw his money in a year when Earth was a post-apocalyptic wasteland ruled by the Daleks.
This has been said of the Doctor himself, in the Doctor Who Missing Adventures novel The Crystal Bucephalus. He explains that to avoid drawing too much attention, he occasionally has to invest huge sums in doomed business ventures (such as the time-travelling restaurant of the title) and the British film industry.
In Goodnight Sweetheart, this gets tried using the portal that connects contemporary London with war time London, but the company that they invest in split in the 50s and, without any contact from the investors, the bank puts the shares in the half of the company that folded.
A case of research failure: in real life he would have ended up owning shares in both spin-offs.
A non-time travel example: an episode of the Highlander tv series shows Duncan taking advantage of his immortality with this strategy. Thanks to his "great-great grandfather" depositing 10,000 francs, his account holds over a million. Humorously, one time when he tried this the bank was robbed while he was in the middle of cashing out the account. So much for that idea...
Which does not take into account that in the meantime there was at least one devaluation of the Franc, at a cut of 100:1
In a Red Dwarf episode, it is revealed that Dave left £17.50 in his bank account on Earth. Three million years have passed, and he now owns 98% of the world's wealth. He also left a sausage out on his table which went mouldy; now the mould covers seven-eights of the surface of the Earth. Furthermore, he left the lightbulb in his bathroom, racking up a gigantic debt to the local utility company, which has now become the ruling faction on Earth and whose battle fleet is rapidly approaching in an Attempt To Collect. It turns out to be a joke by Holly.
Mentioned in the American version. Lister's first words after being informed that he's been in suspended animation for almost three million years involve exclaiming that his baseball cards must be worth a fortune.
In the original version he also laments that he has an unreturned library book.
In an episode of Sabrina the Teenage Witch, Sabrina's aunts explain how they got rich: junk. When you live hundreds of years old, it's easy to buy worthless commercial junk made by the hundreds of thousands of units and put it away for a few hundred years until age and scarcity turn them into priceless antiques. They add that the Mickey Mouse plates they just bought will be worth millions in a few centuries.
Subverted in Star Trek: The Next Generation. A businessman who was cryogenically frozen during the 21st century arranged for a firm to manage his account, expecting to awake to a great profit. As it turns out, a third World War and conversion to a currency-less economy left any remnants of his accounts worthless.
While he's upset at this, he doesn't realize that he can get anything he wants just by talking to a replicator. In an Expanded Universe novel, he becomes the Federation ambassador to the Ferengi, given his rather unique skillset and understanding of the capitalist mind.
Played with in an episode of The Twilight Zone. Four thieves steal gold and freeze themselves for a hundred years, thinking they will be able to claim their riches after everyone has forgotten about the crime. Turns out that the crime has been forgotten, but in the future gold can be cheaply manufactured and is therefore worthless. Their intent is different (hoping to avoid interest rather than earn it) but the result is the same.
Discussed briefly in an episode of Being Human when Vegetarian Vampire Hal reveals that he has little to no money Tom asks why he didn't just get a bank account, because being immortal and everything even if there had been periods of massive inflation or something then he'd still have a small fortune.
Forms a Brick Joke in the Stargate SG-1 episode "1969". After SG-1 is sent back in time to the eponymous year courtesy of an interaction between the stargate and a solar flare, Jack borrows some cash from the future General Hammond, then a lieutenant, and promises to pay him back with interest. When they get back to 1999, Hammond tells Jack he owes him $539.50, including interest.
Supernatural. When Sam and Dean travel back to 1978 in "The Song Remains The Same", Dean off-handedly suggests they invest in some Microsoft stock while they're at it. Sam says they may have to if they can't find a way back.
To Art Dankwalther, I leave the sum of 34,586,224,739.58 in UCAS dollars. According to my calculations and accounting for conversion of the original currency, inflation, and 1 percent interest per annum, this settles my debt to your ancestor for the gold piece he kindly lent me for the last meal we shared.
The Time Travel based RTS game Achron has a variant of this known as 'Retconomy'. One of the playable species creates harvesters by morphing one of their basic units. These basic units can be built and paid for in the future and then sent into the past where they become harvesters and begin gathering resources. The end result is that the player will have gathered more resources in a shorter amount of... er... time than a player that had not used time travel.
It's possible to pull this trick off in Animal Crossing. Deposit a reasonable sum of Bells in the bank. "Time travel" by setting the system's clock as far forward as it will go. Go to bank and check sum. Profit! Then you can travel back in time and safely keep your vast fortune. The downside? Your town will become a depopulated, weed-ridden wasteland, of course.
A strange case of banking and time travel is possible in The Legend of Zelda: Majora's Mask. Link has the ability to rewind time 72 hours before a certain point in-game time, and predictably, when he rewinds time he loses all of the money he accumulated during that 3-day period. Fortunately for Link, the hub city's bank is apparently temporally insured, since the banker stamps Link's account balance on his hand, and this stamp never fades or disappears with the rewinding of time. Realistically, this should mean the complete destabilization of the city's economy, since the money deposited at the end of the 3-day cycle technically does not exist at the beginning of the cycle, but most people are probably more worried about the moon falling out of orbit than they are about time-travel based banking scams.
As long as the banker had about 5,000 Rupees in reserves at the beginning of the cycle, Link would be able to withdraw it all without causing a bank failure. Whenever he resets time, the Rupees go back to the banker, so he's really just borrowing the Rupees; in three short days, the city's economy can't be ruined by just 5,000 Rupees.
Can be easily performed in Fable II right after the mains story begins. Rent out your caravan for a measly few gold, then set your clock forward a few decades. Use that money to buy more property, repeat, and you can own all of Albion the moment you lay eyes on it.
Dave Strider of Homestuck has the LOHAC Stock Exchange in his back pocket thanks to this trope.
Spinnerette has a time-traveling Benjamin Franklin use this as a means of obtaining start-up capital for the modern-day superhero support organization he runs in the present day. Interesting, its stated that the money wasn't that much, only enough to get things started, and most money comes from merchandizing deals.
In Casey and Andy, Jenn always carry a small supply of gemstones in case she ends up travelling through time or dimensions (which is very, very often for her) because they are almost always valuable and can be sold for legal tender with minimum hassle. Of course, the main reason she carries jewels is she is a professional jewel thief.
In 21st Century Fox there was a Chinese space station full of dissidents who wanted to freeze themselves at an "abandoned" North Korean moonbase for 500 years in the hopes that China would have more women then, and use their accrued interest to live like emperors. After Jack escapes from them he hacks their bank accounts and donates their money.
Dr. Steve tries a variant of this in The Adventures of Dr. Floyd. While he's always got a time machine and is trying to sell various things on ebay for profit, one time he simply bought 100 copies of Action Comics #1 and tried to sell them when he got back to the future. The problem is he neglected to seal them properly and they disintegrated!
An odd variant in Back to the Future: The Animated Series: Jules and Verne travel to 2091 and have to take a cab, but find out the cab fare is very high. The only money they have is a quarter; however, it turns out that a 1983 quarter is a rare and expensive collector's item by that point in time. The cab driver skips away in glee at his new fortune.
inverted in The Flintstones: Fred borrows 4 dollars on his paycheck so he can have a long weekend with Wilma and the Rubbles, thanks to the Great Gazoo, they get sent to a very Jetson-like future, while he's in the future, he visits his employer, and discovers that he owes his company 23 million dollars.
In Futurama, Fry becomes rich overnight when he goes to the bank for the first time in a millennium and discovers that he's rich beyond imagination, but he falls for an elaborate scheme to steal his money after he obtains the world's last can of anchovies, which would then be used to buy them off him. He ends the episode as broke as before.
To throw another monkey wrench into the works, he wasn't actually trying to get rich. He just needed 50 cents and realized he still had just under a dollar in the bank.
The Stable Time Loopplan on Gargoyles that helped make Xanatos part of the Fiction 500 comes close to this trope. Xanatos went back in time and earned a practically worthless coin that he then had the Illuminati Society deliver to a David Xanatos 1,000 years later... when it was worth 20 grand. The rest was investments.
Which was also part of his lesser plan to prove to his father that he was a "self-made man".
Double Subversion on South Park, where the money saved this way was almost worthless in the future due to inflation, but it was still better then the grinding poverty most people suffered from.
If you invest in the right assets, this can work. See the Louisiana Purchase, the Alaska Purchase, and probably most impressive, Manhattan, bought for about $1000 (2010 purchasing power).note The initial payment was to tribes that didn't even own the land. They just had a deal with the actual owners to hunt there. A later, larger payment was made to the angered actual owners of the land.
Benjamin Franklin did this without time travel. He bequeathed £1,000 each to the two most important cities in his life (Boston, where was born and raised, and Philadelphia, the adopted hometown where he made his name). Each fund was to be invested by giving loans to young craftsmen for a period of 200 years; each city could take 75% of the fund out after 100 years for a public-works project, and the trust would reach maturity and be given over entirely to the city after 200 years. The Boston fund, when opened, was enough establish a large trade school after the first 100 years; the Philadelphia fund was used to fund scholarships to local high school students at maturity in the 1990s. Please note:
The money wasn't just sitting in a bank, but being loaned out at interest to worthy craftsmen. While in theory the bank does this with the money in a savings account, the interest on the loans accumulated directly to the account, rather than mostly being taken as profit by the bank.
Over the first 100 years, money was fixed to the supply of precious metals; inflation was not constant. In fact, there was fairly constant deflation from about 1870 to 1890. This meant that interest alone could substantially increase the real value of your money. Actually, in periods of deflation, just having money increased the real value of the money; the interest from the loans was just gravy.
Most banks have an inactive account upkeep fee of a couple of dollars a year. Before partaking of this scheme, make sure you have enough seed money to generate more interest revenue than these fees will deduct every year.
More importantly, don't forget Ridiculous Future Inflation. Bank accounts tend not to keep up with it, and there's no point in investment $100 and turning it into $1,000,000 if it's only worth $1.
Even more importantly, certain locations may have laws about inactive accounts, that state that after a certain amount of time without any activity the account may be considered abandoned property and collected from the bank by an appropriate government agency. The accounts will then be held until someone with proper ID claims it. An example from New York State.
A few people tried and failed at this. It turns out, people don't like the idea of someone investing money for so long that they control the economy, and they're willing to change the laws to stop it.
In 1562, the German town of Mittenwalde loaned the town of Berlin 400 guilders at 6% interest, compounded annually. They would like to be repaid. With interest, Berlin owes Mittenwalde approximately 97.7 trillion guilders. Oh, and one guilder is equivalent to 280,000 euros (in 2012). So Berlin's total debt comes to over 27 quintillion euros. Which is more than they have; indeed, it's more money than all the money in the world (The world economy is measured on the order of tens of trillions. A trillion is millionth of a quintillion).
U.S. tax laws are such that if you're an immortal 'inheriting' your own assets, the basis for those assets, which is used in calculating capital gains tax is 'stepped up' to the value on your 'death'. (Example: You buy a stock at $1, fake your death when it's at $31,'inherit' it and sell at $32, and pay tax on your $1 capital gain instead of on $31.)
The caveat is that the Federal Government imposes a 40% estate tax on estates greater than $5.25 million, and many states have their own estate/inheritance taxes. This will cap the ability to pull this trick off.