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Losing one's Geo is a terrible thing and it's so much more likely if you carry it about on yourself.
My vault is much more secure. In all my time as a banker, I've never lost a single Geo!
Maybe you'd considered opening an account?
Millibelle the Banker, Hollow Knight
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Several video games have a currency that the player can use and hold. In most games, the complexity of the money system stops here.

Other games are deeper in their simulation of money: some avoid the Wallet of Holding, limiting the amount of money the character can carry on them with a Cap. In some games, the player is able to put their money in an account they can access from one or even several other places in the game. While some games have these accounts solely to store money, in other games interest is applied to these sums, allowing the player to slowly earn more money thanks to their savings. More advanced versions allow the player to invest in more risky products, allowing them to earn much money but also to lose their funds.

It's most typically used as a Anti-Frustration Feature whenever the player experiences a Game Over or Total Party Wipe and is allowed to continue playing without losing game progress. While some or all of the money on hand will be lost in exchange for resuming game progress; anything stored in the bank is safe.

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In other games, the player can borrow money to fund purchases. Such loans are to be reimbursed, and the player might suffer consequences for failing to repay them, such as being attacked by goons. One of the consequences might be having to Work Off the Debt.

Other, more fringe banking services might be provided, such as life insurance (delivering money on the death of a character) or financial markets allowing the character to put their money on the stock market and bet on the rise of financial assets.

A large amount of Simulation Games (especially Construction and Management Games and Space Management Games) usually offer the player a form of loan system. These either tend to be individual terms that are slowly paid off over time (or repaid when possible), or an amount that you can borrow in increments for an indefinite period of time until you repay but it will continuously draw interest until it is repaid.

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See also An Entrepreneur Is You, Money Sink (the payment of interests might be interpreted as such) and Arbitrarily Large Bank Account.


Examples:

Action-Adventure

  • The Legend of Zelda: Majora's Mask features a banker in West Clock Town whom Link can talk to as a means of depositing and withdrawing rupees which will remain saved even when Link uses the ocarina to reset back to day 1. Having a total of 200 rupees in the bank will reward Link with a bigger wallet while 5000 earns a Piece of Heart.

Eastern RPG

  • Pokémon Gold and Silver allows storing part of the money earned during fights with the player's mother. Once enough money has been saved, the player's mother can give several gifts, including rare items.
  • Jimmy and the Pulsating Mass has a bank that stores money, giving a 20% interest rate, which is useful because of Adam Smith Hates Your Guts. Moreover, you need $100,000 in your account to enter a certain side dungeon.
  • Bug Fables: The Ant Bank offers 2% interest on deposited berries for every 30 minutes of play time. Depositing 500 berries for the first time will upgrade you to the bank's Platinum Card membership and double the interest. Up to 10,000 can be deposited.
  • EarthBound: ATMs let you store your money in a bank account, where it is safe in the case of a game over. Half your pocket money is lost at a game over. It's also how the game plays with the use of Money Spiders: when defeating enemies, instead of cash immediately going to your party's inventory, Ness's dad deposits money to your account.

Massively Multiplayer Online Role-Playing Game

  • EVE Online players proposed banking services though, as befits the universe, all of them were frauds, whether by conception or by execution: since players had no way to ensure the bankers would actually pay up capital and interest and the bankers themselves had no way to force debtors to pay up their loans, along with the fact the game had plenty of liquidities circulating, banking was simply unpractical for the time being.
  • Final Fantasy XIV has Retainers, NPCs who the player can customize and act as a money and item bank. On top of that, you can only sell in the player market (called the Market Board) through them, and if anyone buys your items, the Gil gainied will be automatically stored through that Retainer.
  • In RuneScape, players can deposit and withdraw both money and items from banks in-game.
  • The Averted Trope is actively enforced in Second Life: due to the fact the company could have faced additional regulatory hurdles since L$ could be converted into real money and that most of the banks which opened inside the game were unsustainable ventures (due to the lack of investments able to pay for these rates) or outright Ponzis (for example, the infamous Ginko Financial gave interest rates as high as 0.145% per day or 69.7% per year), no player can open any bank (defined as any institution accepting funds and promising to pay interest) inside the game, unless they get an official authorisation from public regulators.
  • Star Wars: The Old Republic has this with a bit of Loophole Abuse. Free-to-play players have a cap on how many credits they can carry, with any excess going into an "escrow" account. Getting the credits out of escrow requires either Cartel Coins (i.e., real money) or subscribing. However, everyone can have a Legacy Cargo Hold, a money and item stash shared by all characters on an account. The credits in this stash are not capped, so you can use it as a bank to deposit your credits before you hit the cap.

Metroidvania

  • Hollow Knight: Millibelle the Banker can be found near Queen's Station offering her services. It's actually a scam, and she runs off with your money if you deposit more than 2500 geo.

Party Game

  • The Jackbox Party Pack: "Bidiots" has the hilariously-honestly-named Predatory Loans company, who will, up to twice per game, loan you $1,000 cash, in exchange for paying back $1,500 at the end of the game.

Platform Game

  • Super Mario Galaxy 2 features the Banktoad, who holds on to Star Bit deposits and allows the player to share them with other save files.

Roguelike

  • Scarab of Ra: Some of the texts on walls throughout the pyramid will turn out to be deposits where you can bank your money. In this game, money has no purpose except increasing your score; if you die then you lose a percentage of the value of any money you had on you. Banking ensures that you get the full value, and also means you don't have to carry it around — gold is very heavy.
  • NetHack: Shop owners will run out of money and offer store credit for further items you sell to them.
  • BPM: Bullets Per Minute: A Bank room may spawn on any floor. You can deposit or withdraw coins from here, and the balance in your account persists between runs.

Simulation Game

  • Animal Crossing: You earn interest on the money in your bank account every month.
  • Yes, Your Grace: The Bank of Florentini provides loans of both gold and food supplies that need to be reimbursed in fixed installments over the following weeks. Barring the very first loan taken, the interest takes the form of an extra installment after the money has been paid back.

Stealth-Based Game

  • Assassin's Creed: In Assassin's Creed: Syndicate, all proceeds from the Rooks' criminal activities are deposited into a safe on the Jacob and Evie Fry's train. The funds increase roughly once an hour and the player is notified once it has reached capacity, at which point no additional funds will generate until a withdrawal is made.

Third-Person Shooter

  • Splatoon 2: Octo Expansion uses a currency called CQ Points, which are required to access the various stations of the Deepsea Metro. If you run out of points and need more to continue, Pearl will let you take out a loan of 3000 CQ Points. These loans don't accumulate interest and you can take out as many as you want, but having an outstanding balance will restrict you from unlocking certain features until you've paid it off.

Tower Defense

  • In the Bloons Tower Defense series, the 2nd path upgrade for the Banana Farm is called the Monkey Bank. It gains in-game money over time and this money can be withdrawn at any point. If you build multiple Monkey Banks, you can withdraw all their money at once. They can be further upgraded into the IMF Loan and Monkeynomics, which have higher carrying capacity and allow you to loan out some money, although you have to pay it back. There's also a Monkey Knowledge upgrade that lets you deposit money into Monkey Banks and their upgrades, to get even more later.

Turn-Based Strategy

  • Taipan!:
    • The player can get loans at extortionate rates from Elder Brother Wu. In the Apple II version, if you pay back Elder Brother Wu more than you owe him, he starts paying you interest on the extra money and you can withdraw it, though Wu still send you his thugs to ask for repayment. This makes him much better than the regular bank of Hong Kong.
    • While in Hong Kong, it's possible for the player to deposit any of his current cash on hand in a bank or withdraw cash in their account. The bank pays a small amount of interest. Cash is only safe from being stolen while in the bank.

Web Game

  • Board Game Online features a bank the player can either store their money in, get life-insurance from, or attempt to rob.
  • Neopets features the National Neopian Bank as a means of saving Neopoints and preventing them from being stolen from various means. Interest can also be collected daily, and the more money saved, the more the bank pays you interest. Also, just like real banks, there is a limit to how many times one can withdraw per day.
  • In Stick RPG 2, the Dimension Banks location allows you to store and deposit money in an ATM. You slowly gain interest over in-game days. If you have enough money, you can even buy out stores or purchase new houses.

Wide-Open Sandbox

  • In Fallout, the Friendly Loaning Company can give to the player loans with a 10% daily interest, with ten days to repay.
  • In The Elder Scrolls II: Daggerfall, money has a weight. The game has an extensive banking system to allow players to transfer their wealth into notes of credits. You can also put it into a bank account, but each region has their own separate banking system and the only purchases that can draw directly from the account are houses and ships (as those are bought from the banks themselves).
  • Grand Theft Auto V has Maze Bank, a service the player can access using the in-game cell phone to deposit or withdraw cash at any time. The player can also buy and sell corporation shares, whose values fluctuate depending from the player's option.
  • SunDog: Frozen Legacy: Each star system has a Uniteller network, and you can send money between systems using it so that you don't have to carry cash. If you lose consciousness (due to mugging, lack of food, or lack of sleep) then any cash you're carrying will be stolen.
  • In The Witcher 3: Wild Hunt, the Vivaldi Bank allows Geralt to exchange Nilfgaardian Florens and Temerian Orens for Novigradian Crowns. Geralt is also able to take out a loan, but each loan must be paid in full before another can be requested.
  • Both the original Uncharted Waters and Uncharted Waters: New Horizons capped how much gold you could carry with you at any time, forcing you to deposit the excess in a bank. In the first game, you could only store your money at the palace of the monarch you were currently loyal to (king of Portugal by default), while in the sequel, most major ports had a dedicated bank building where you could deposit and withdraw money, with the extra benefit of a small interest rate.
  • In Enderal, the city of Ark includes a bank which offers various services, one of them being a personal account which offers a daily 2.80% interest rate; interest are capped at 250 Pennies per day, making pointless to store more than 8928 Pennies. Other services include a vault (a personal storage vault for the player character, as well as NPC vault than can be accessed through theft or quest reward), shareholding in a few businesses (obtained through quest reward or thieft, result in bonus daily account income added to the daily interests), house buying, and a merchant (sells skill books and blueprints).

Western RPG

  • Divinity: Original Sin II: A kindly old lady in Arx will loan out princely sums, in exchange for a phial of the debtor's blood and the promise that they will die if they don't repay the debt, plus interest, upon her request. She's actually a demon in disguise.
  • Might and Magic: The third game has a bank in the first town. It's only open during daytime hours. You can deposit gold and gems there for safekeeping but as days go along, you'll slowly accrue interest on both. Regular deposits plus careful planning can result in a load of gold and gems for your party by game's end. The sixth game's banks do not pay interest, which is said to be due to the economic crisis in Enroth, but serve to protect your gold if you die(since death results in you losing all the gold you have in your inventory).

Non-Video Game examples:

Tabletop Game
  • Scum and Villainy caps how many credits the crew can carry in cash at any time, but lets you borrow from Loan Sharks if you ever need more than that. The interest on that debt is 100%, however, so for every CRED you borrow, you have to pay two back, and if you don't do so within a certain in-game time, the lender will send Bounty Hunters after you.
  • Traveller allows players to take out mortgages on their starships, worth tens of millions of credits at minimum, usually splitting the price into 480 monthly payments of 1/240th of the cash price. However, this has led to a Fan Nickname of "Spreadsheet: The RPG", especially in a free trader campaign.
  • Dungeons & Dragons, module B2 Keep on the Borderlands. The Keep has a Loan Bank where a Player Character can take out a loan with an interest rate of 10% per month (that's 214% or 120%, depending whether the interests are compounded or not, per year!). If the loan amount is over 5 gold pieces, the PC has to turn over collateral with a value of at least twice the amount of the loan.
  • Arkham Horror: Investigators can take out a bank loan, but until it's repaid in full, they have a 50% chance per turn of being required to pay interest or lose all their items.
  • Eldritch Horror: Investigators can gain extra money at the cost of a Debt that might come due at any turn. Consequences range from getting roughed up by goons to being forced to abet Apocalypse Cultists.
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