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Why do banks pay a compound interest on deposits?

Obviously they'd be better off paying a simple interest instead, which would still be attractive to their customers.

However I figured that in such a situation, I could simply deposit money in a bank, say, for a year, earn the interest for that year, withdraw the original capital plus the interest, deposit it in another bank, earn an interest on the interest of the previous deposit and so on, thus getting to enjoy a compound interest anyway. Obviously in this scenario a single bank wouldn't enjoy long term deposits, which is why they'd rather pay a compound interest to their customers.

Is my reasoning correct? And are there other reasons why banks pay compound interest?

The answer to this question doesn't seem trivial.

Despite my efforts, I could not find any useful resource on the internet to answer this question. Useful resources are very welcome.

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    The simple answer is that compound interest is simpler.The bank only has to keep track of the current balance. – Pete Becker Aug 4 at 13:28
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    @kYuZz You're assuming the rate offered doesn't already take into account how much the bank expects to pay in interest. If banks used simple interest, they could offer a higher rate (which would certainly appear more attractive to customers) without increasing the amount of interest the bank has to pay. So then the question becomes, why don't banks do that? And you get back to "compound interest is simpler"; the cost of managing simple interest outweighs the advertising value of a higher rate. – chepner Aug 4 at 13:54
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    That's why they often advertise APY instead of APR, the marketing allure of simple interest without the fuss. – Hart CO Aug 4 at 14:27
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    @kYuZz Really? They wouldn't let you withdraw and deposit money in your own account? Are they even a bank, then? – user253751 Aug 4 at 16:01
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    It's not even that it's simpler, or more competitive, really. It's just that (unless they regularly send you the accurued interest), bank accounts are always going to compound. The only thing that changes is the compounding period. Your money's in the account, it earns interest that's payable after a certain time. Put that interest in the same account, and you're compounding. – jamesqf Aug 4 at 17:19
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I don't think there's one definitive answer, but certainly your scenario is an appropriate interpretation of compound interest. You wouldn't even need to change banks; just make a complete withdrawal and immediately redeposit it.

But primarily, as Pete eloquently put it in a comment, compound interest is simpler.

Remember that banks have been around for hundreds of years, before computers made bookkeeping trivial. It's likely that it was much simpler to just track the entire balance of an account and pay interest on that rather than having to account for "principal" and interest separately and pay interest only on the principal. You'd also have to keep track of withdrawals, and somehow portion the withdrawals between interest and principal.

Also note that banks also get to charge compound interest on revolving debt like credit cards (but typically not lines of credit). The interest changed is added to the account, and your interest is calculated on the entire balance, not just the "principal". So it works in their favor as well.

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In a sense, banks don't pay compound interest, they just pay interest at the end of a certain period. If you leave your original deposit and the interest they paid for that period in place for another period, then the pay interest on both the original deposit and last period's interest. This way, the interest begins to compound: in the second period, you get interest on the interest; the period after, you'll get interest on the interest on the interest etc.

(Things are slightly complicated if they, say, calculate interest on the daily balance, and only pay it monthly, but that's just "detail").

Also, as chepner notes in a comment, market forces will tend to mean they will end up paying "the same amount of money" either way, whether it's calculated as simple interest at one rate, or compound interest at a different rate.

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    Simple and compound interest rates can be set so that they have an equivalent payout, but only at a specific point in time - before that, simple interest will pay more, and after that, the compound interest will pay more. The bank would have to have an accurate estimate of how long customers leave their money in the bank to set the rate properly, and as long as at least some banks offer compound interest, rational customers should switch (or reinvest their interest) after the break-even point. – Nuclear Wang Aug 4 at 14:52
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Compound interest encourages longer-term investments.

Banks want to hang onto as much of your money for as long as they can. With simple interest, you get the exact same interest payout every day/month/year - it doesn't matter how long the money has been invested. After putting some money in a bank account with simple interest, I have the same incentive to keep it there after 1 year, or 5 years, or 10 years. I can withdraw the money, and reinvest it a year later, and lose nothing more than that single year's value in interest.

With compound interest, your interest payout goes up with each passing day/month/year, as your principal compounds and the value of the interest goes up. Because of this, my incentive to keep my money in the bank is constantly going up. I stand to earn more interest in year 2 than I did in year 1, so I'm effectively incentivized to keep my money in the bank for as long as possible, in a way that simple interest does not. If I withdraw money for a year, I'm missing out on that year's interest, plus all the future interest I would have earned on that year's interest.

Simple interest and compound interest rates could be set such that they have an equivalent payout, but only at a certain point in time. Before that break-even point, simple interest would pay more, and after that point, compound interest would pay more. A savvy investor could invest in a higher-yield simple interest account, and simply close it and reinvest or switch to a compound interest account that would have a higher long-term yield. Simple interest doesn't expressly prevent one from taking advantage of increasing principal, but it puts an onus on the consumer to constantly close/open accounts or expressly reinvest interest as principal.

Overall, compound interest is easier for the consumer since they don't have to muck around with their account to maximize interest, easier for the bank since the bookkeeping is simpler, provides a potentially larger long-term benefit to the consumer, and provides a means for the bank to incentivize long-term investments.

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You can get your scenario in any bank: invest in a certificate of deposit, and on maturity, roll over the CD into a checking account that doesn't qualify for interest.

Sure, to your leading question, a bank would be happy to keep you as a customer if you leave the money in the non interest bearing account. But they can't compel you to leave the funds there (where they can keep you in the CD until maturity with forfeit interest or fees).

If your stated plan is to roll over the proceeds of the CD including interest into another one, or the same setup at the next bank down the street, then let me tell you this exciting news: banks have savings accounts that do this for you, on the granularity of 1 day than one CD term. The interest rate on each day may vary as a function of the federal funds rate or marketing decisions (where the rate set for the CD won't change over the term) but it automatically rolls over, and compounds daily.

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