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For a large proportion of loans, why is interest paid on the outstanding amount instead of the entire amount of a loan?

For example, for a 100.000 loan with a 10% interest, basic logic would imply that you have to pay back 110.000. But you usually pay less because your first repayments contain more interest which decreases as the remaining amount of the principal decreases.

I imagine that when loans were first invented, that's how they worked. I doubt goldsmiths would build a repayment calendar for their borrowers. You knew what you had to pay back by a simple multiplication operation. Now the financial products are more complicated and need more complicated calculations to know what you need to pay back.

What are some of the reasons a lot of loans work like this now?

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    what is the length of the loan? for a multi year 100,000 loan at 10% you will pay a lot more than 110,000. – mhoran_psprep Nov 20 '19 at 15:12
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    Why would I want to pay interest on money I've already repaid? – chepner Nov 20 '19 at 15:19
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    That's a separate question: did I agree to that? The terms of the loan spell out exactly when and how interest is calculated. I may be willing to forgo any payments until the entire loan is due, and I may be willing to pay interest based on what I currently owe, but I'm certainly not going to take out a loan on which I am charged interest on a portion of the balance I have already paid back. – chepner Nov 20 '19 at 15:32
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    You can stretch the repayments over multiple years and still keep the same amount no you can't, not without changing the ultimate value of the loan. Interest is inherently a rate not a fixed amount. It is dependent on principal and time. If you take longer to pay back, you owe more. – dwizum Nov 20 '19 at 15:33
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    Put another way: why would I ever start paying the balance back early if I couldn't reduce the interest owed by doing so? – chepner Nov 20 '19 at 15:35
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In a comment, you provided the following statement - which I feel is critical to understanding where your logic is breaking down (when compared to typical modern lending practices):

You can stretch the repayments over multiple years and still keep the same amount

The point you're missing is that interest is presented as a rate. It has a numerator and a denominator. It is dependent not only on the amount of money that was borrowed, but also the time that it takes to pay it back. Interest is expressed as a percentage of principal per unit of time. If a lender agrees to 10% interest, it's typically either explicitly stated what the denominator is, or it's advertized as an effective rate (i.e. an effective annual rate, implying the denominator is "per year.").

There is effectively no such thing as a loan where the interest is fixed to a certain dollar amount, but the term (the length it takes the borrower to pay back) is completely arbitrary.

The reason why this is typical practice is because lending is built (somewhat) on the idea of money having a time value. A dollar today is equivalent to a dollar plus some small amount a year from now, and a dollar plus a larger amount ten years from now.

In the comment I quoted, you seem to be implying that loans are structured based on calculating a total interest amount due, and then - separately - setting the term over which the loan will be paid. Because of the time value of money, you cannot separate rate and term. To put it simply, there's no sense in quoting a rate unless you know the time frame for which it is effective.

In further comments, you suggest that in order to get around this, a lender could raise the rate to something higher if a borrower wanted to take more time. Effectively, by allowing for that, you're just implementing a more complicated version of the current standard approach, by separating rate and term and then iterating. It's much easier for consumers and lenders to just have one discussion based on the typical concept of a rate being effective for a given unit of time. Also, this makes marketing and pricing more streamlined, because it's easier to compare rates from lender to lender if they're all structured based on the same unit of time.

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    The fact that you could be doing something else with the money (over a period of time) is the basis for time value of money. We expect money to "grow" over time because we do things with it, regardless of what those things are (invest it, lend it, etc). – dwizum Nov 20 '19 at 15:49
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    Ah, yes. I thought the TVoM was because of inflation. – RonJohn Nov 20 '19 at 15:56
  • I'm sure there's an argument that it's related but now you're venturing into economics theory which is beyond my (loan-pricing-based) sphere of knowledge! – dwizum Nov 20 '19 at 15:58
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For example, for a 100.000 loan with a 10% interest, basic logic would imply that you have to pay back 110.000.

No. The interest rate is usually given per year, so for each year I owe you 100,000, I owe you an additional 10,000.

But I don't owe you the full 100,000 all time long. If I pay you 20,000 at the end of the first year (10,000 interest and 10,000 repayment) I owe you 90,000. So I am in the same situation as if I had taken a 90,000 loan at the first place, so why should I pay you then 10,000 for the 2nd year? I owe you only 90,000 now, so it is simple logic that fewer interest is due.

Or again, in a different way: For the numbers, it is exactly the same as if I took a loan for 1 year. At the end of that year, I pay 20,000: 10,000 for interest, 10,000 for repayment, and I take another loan for 90,000. So the old loan is gone, and I have a new one for 90,000. On this, of course I have to pay only 9,000 if the same interest rate of 10% applies.

In order to expand a bit on this: There are several types of loans:

Interest only loans are what they are named: on them, only the interest is payed. On a 10 year interest-only loan of 100,000 for 10%, each year I have to pay 10,000 of interest. At the end, I still owe 100,000.

An annuity loan, however, is calculated differently: here I pay a fixed amount every month which includes interest and a bit of repayment. Because of the now smaller principal, the interest part is a bit less every month and the repayment part a bit more. This way, repayment starts slow and ends fast.

  • One could argue that an "annualized" rate is just a market convention. I could set up a loan where you owe be 10% of what is borrowed whether you paid it off in one day or 10 years. – D Stanley Nov 20 '19 at 15:16
  • @DStanley Of course it is. But you wouldn't be happy if I extended this time to 20 years. And some contracts indeed are this way: early payments are either not possible at all or come with a penalty which includes the expected interest of the borrower. – glglgl Nov 20 '19 at 15:20
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The question conflates loans like bonds with loans like mortgages.

A bond works like the example, borrow $100,000 and pay $10,000 in interest each year. At some point, the borrower has to pay off the $100,000.

A mortgage is named such because the loan dies or ends (mort = root for death in romance languages). It is designed to have a constant payment where part reduces the loan and the rest is interest for that period on the total loan remaining. At the end of the term, it's over. You need to be reasonably good at college level math to do the calculation but for the rest of us there is Excel's PMT() function.

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What are some of the reasons a lot of loans work like this now?

Very simply: Regulations.
You won't find a loan where you get quoted an amount as interest. You won't find a loan where you get quoted a percentage as interest. Loans were regulated (to be more transparent) to advertise Annual Percentage Rate (APR). Further, banks were regulated on the way compounding works.

The way you describe only works in very specific circumstances. You need to have a specific payment date. If your loan has to be repaid in 2 weeks (such as payday loans, which incidentally still tend to work that way), you can specify total interest. You also don't want to advertise that your 14% interest for the 2 weeks comes down to 500% APR.

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No, the low initial repayment fee is not how typical loan works. In fact, such loan repayments scheme is a leverage tool to encourage property flipping activities for under-development property to fuel property bubbles.

Using the $100k loan 10% interest 10 years loan for example, for a property that is still in development and only complete in 2 years, banks may give borrower following repayment options

Option 1. Pay only the interest fees in the first 2 years when the property is still under development. Only pay back the principal and interest after the property is ready (i.e. the 3rd year). The Borrower will pay $833.33 monthly for 2 years, then pay ~$2023 monthly when the house is completed. Total payments for 2 years are $20,000.

Option 2. Served the principal and interest fees immediately, from the beginning, pay $1666.66. Total loan repayments for 2 years are ~$39,999.

For a real house owner, Option 1 means paying extra $20,000 interest fees for 2 years for no reason. So select option 2 is the most rational things to do.

But in a flipper scenario, if the flipper can flip the property from $100K to $150K in the 9th months, the flipper actually pay $7500, and making $42,500 in profits (150,000 - $100,000 - $7500).

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