<p>Interest payments are contractual payments. They need to be specified with an exact formula. For a given set of cash flows, one could come up with a multitude of formulae that end up giving the same values. In order to make interest rates comparable, laws, regulations, and market conventions specify that different conventions be used.</p>
<p>Of these conventions, simple and compound interest are possible choices. For simple interest, the interest payment is just the interest rate times the principle times a time factor. Compound interest takes into account increases in principal.</p>
<p>If a loan has associated interest payments that must be paid immediately, the loan resembles a generic bond: principal amount does not change. Bonds have a wide variety of conventions to convert the price of a bond to a yield, including a “simple interest rate” convention. However, changing the convention does not change the contractually defined price or cash flows. Since generic bonds do not roll interest payments into the principal, “compound interest” does not make sense.</p>
<p>For loans, interest is often rolled into the principal. We can then use simple interest or compound interest conventions.</p>
<p>Assume a monthly frequency, with no calendar date irregularities, for a loan agreement.</p>
<ul>
<li>The interest rate could be specified as a simple interest rate of 1% a month.</li>
<li>The interest rate could be specified as an annual compound interest of <span class="math-container">$1.01^{12}-1$</span> or 12.68% (approx).</li>
</ul>
<p>Regardless of the convention used, if the borrower makes no payments for a year, the principal will grow by (roughly) 12.68% since the lender will roll the interest into the balance at the end of the month, and then make the simple interest calculation based on the new balance. That is, lenders will still charge interest on interest in practice.</p>
<p>Which one to use is purely a cosmetic decision - is it easier to work with 1% a month, or 12.68% a year?</p>

CC BY-SA 4.0
2021-02-26T12:22:05.123Z
2021-02-26T12:22:05.123Z
Brian Romanchuk
<p>This is just an addition to <a href="https://economics.stackexchange.com/a/42772/31887">Brian Romanchuk's answer</a>, caused by the fact that recently I stumbled upon the paper [1] by <a href="https://link.springer.com/article/10.1007/s10203-010-0102-y" rel="nofollow noreferrer">Eugenio Levi</a>. In the article three conceptions about the concrete meaning of interests laws are analyzed, and in §5, p. 156, where some consideration on interest laws as contracts are offered, the Author states that</p>
<blockquote>
<p>... la maggior parte dei contratti di prestito prevede l'interesse semplice (se si tratta di operazioni a breve scadenza) o il pagamento periodico degli interessi semplici (se si tratta di operazioni lunga scadenza).<br>
<br>
<em>Free Engl. transl.</em>: ... the majority of loan contracts requires simple interest (in the case of short-term operations) or periodic payment of simple interest (in the case of long-term operations).</p>
</blockquote>
<p>Thus it seems that, at least in the fifties of the twentieth century, and at least in Italy (or perhaps in European countries), interests due for loan contracts have been calculated by using simple interests: moreover
following the conception of interest laws as contracts, the author remarks that, in such situations, it is really a matter of taste for such cases to consider simple or compound interest.</p>
<p><strong>References</strong></p>
<p>[1] Eugenio Levi, &quot;Sul significato concreto delle leggi di interesse&quot; [free Engl. transl.:&quot;On the concrete meaning of interest laws&quot;] (Italian), in Walter Bigiavi, Gianfranco Cimmino, Paolo Fortunati, Dario Graffi, Antonio Pignedoli, Mario Villa, Giuseppe Varoli (Eds.), <em>Scritti Matematici in Onore di Filippo Sibirani</em>, Bologna: Dott. Cesare Zuffi Editore, pp. 151-160 (1957), <a href="https://zbmath.org/0077.13406" rel="nofollow noreferrer">Zbl 0077.13406</a>.</p>

CC BY-SA 4.0
2024-01-20T22:51:29.347Z
2024-01-20T22:51:29.347Z
Daniele Tampieri
<p>Recently I started to read again Brealey &amp; Myers's &quot;Principles of Corporate Finance&quot; (an older edition I hold it since I attended to the university course on Economics and Corporate Finance as a part of the curriculum in Electronics Enginering at the University of Bologna), since I need to evaluate the profitability performance of some projects I am involved with. The two authors use the <a href="https://en.wikipedia.org/wiki/Net_present_value" rel="nofollow noreferrer">NPV method</a> which assumes (more or less explicitly) the use of <a href="https://en.wikipedia.org/wiki/Compound_interest" rel="nofollow noreferrer">compound interest</a>, perhaps familiar to all of us, and, en passant, mention the existence of the <a href="https://en.wikipedia.org/wiki/Interest#Calculation" rel="nofollow noreferrer">simple interest</a>. Inspired by curiosity, I searched for applications where the interest rate is required to be simple, but I was not able to find anything outside examples in textbooks and lecture notes, so <strong>my question is: what are the uses of simple interests in current economy?</strong></p>
<p><strong>Edit on behalf of the comments</strong>. I am asking this question because I am curious to see some examples and understand the reason why, in these cases, the simple interest is used. In my understanding, the use of compound interest is extremely natural since it corresponds to the intuitive concept that the invested money (continuously) produces a cash flow that is implicitly reinvested (at least up to the moment when the intial investment + the interest has to be payed back), thus it implicitly generates a (continuous time) conpound interest rate: for the simple interest I am not able to imagine such an intuitive explanation.</p>

CC BY-SA 4.0
2021-01-04T15:08:25.453Z
What do you mean by uses? Both simple interest and compound interest have the same use - they are payments from borrower to lender to compensate  lender for supplying the funds.
1muflon1
CC BY-SA 4.0
2021-01-04T15:11:25.257Z
@1muflon1 I mean specific uses, where the simple interest is (more or less mandatorily) used instead of the seemingly more common compound interest: I was not able to find any particular application requiring that specific way of calculating an interest.
Daniele Tampieri
CC BY-SA 4.0
2021-01-04T15:17:16.373Z
I don’t know of any law that would require simple interest. When you borrow from someone usually you have great deal of leeway in deciding the terms of that loan. I don’t know of any country that would make simple interest mandatory in any case. Some department stores will charge just simple interest but that’s not because it’s mandatory but because most tabs are short term anyway and it’s nice for the customers... I mean is this what you are interested in? In some practical examples? Practically simple interest is scarcely used but you can find some cases
1muflon1
CC BY-SA 4.0
2021-01-04T18:18:47.040Z
Simple interest is a calculation convention. It has no effect on the underlying cash flows. The only reason to use simple interest is if you don’t have access to a digital computer, which is a problem rarely run into after 1990.
Brian Romanchuk
CC BY-SA 4.0
2021-01-07T14:18:41.943Z
@1muflon1 I apologize for my later in answering to your comment: I am exactly searching for some examples and I'dl like to understand the reason why in these cases the simple interest is used. I further edited my question above in order to precise this point.
Daniele Tampieri
CC BY-SA 4.0
2021-01-07T14:21:00.617Z
@BrianRomanchuk therefore is the use of simple interest simply due to the simplicity of the associated calculations? This seems reasonable.
Daniele Tampieri
CC BY-SA 4.0
2021-01-08T02:48:16.957Z
Yes, it’s just a calculation convention, which gives an entirely meaningless answer. Only reason to use it is simplicity. That simplicity was useful before the 1980s, when people were often forced to use tables in books to convert prices to yields, and possibly in things like exams.
Brian Romanchuk
CC BY-SA 4.0
2021-02-26T07:00:44.537Z
@BrianRomanchuk would you like to post your comments as an answer? I am writing a small booklet on the subject and if you do so, I'll be able to cite your comments in the references. Anyway, thank you very much.
Daniele Tampieri
<mathematical-economics><interest-rate><investment>
Uses of simple interest
Daniele Tampieri
# Uses of simple interest

(Asked by: username_0 on 2021-01-04)

Recently I started to read again Brealey & Myers's "Principles of Corporate Finance" (an older edition I hold it since I attended to the university course on Economics and Corporate Finance as a part of the curriculum in Electronics Enginering at the University of Bologna), since I need to evaluate the profitability performance of some projects I am involved with. The two authors use the [NPV method](https://en.wikipedia.org/wiki/Net_present_value) which assumes (more or less explicitly) the use of [compound interest](https://en.wikipedia.org/wiki/Compound_interest), perhaps familiar to all of us, and, en passant, mention the existence of the [simple interest](https://en.wikipedia.org/wiki/Interest#Calculation). Inspired by curiosity, I searched for applications where the interest rate is required to be simple, but I was not able to find anything outside examples in textbooks and lecture notes, so **my question is: what are the uses of simple interests in current economy?**

**Edit on behalf of the comments**. I am asking this question because I am curious to see some examples and understand the reason why, in these cases, the simple interest is used. In my understanding, the use of compound interest is extremely natural since it corresponds to the intuitive concept that the invested money (continuously) produces a cash flow that is implicitly reinvested (at least up to the moment when the intial investment + the interest has to be payed back), thus it implicitly generates a (continuous time) conpound interest rate: for the simple interest I am not able to imagine such an intuitive explanation.

**Tags:** mathematical-economics, interest-rate, investment

> **Comments:**
> **username_1**: What do you mean by uses? Both simple interest and compound interest have the same use - they are payments from borrower to lender to compensate  lender for supplying the funds.  
> **username_0**: @username_1 I mean specific uses, where the simple interest is (more or less mandatorily) used instead of the seemingly more common compound interest: I was not able to find any particular application requiring that specific way of calculating an interest.  
> **username_1**: I don’t know of any law that would require simple interest. When you borrow from someone usually you have great deal of leeway in deciding the terms of that loan. I don’t know of any country that would make simple interest mandatory in any case. Some department stores will charge just simple interest but that’s not because it’s mandatory but because most tabs are short term anyway and it’s nice for the customers... I mean is this what you are interested in? In some practical examples? Practically simple interest is scarcely used but you can find some cases  
> **username_2**: Simple interest is a calculation convention. It has no effect on the underlying cash flows. The only reason to use simple interest is if you don’t have access to a digital computer, which is a problem rarely run into after 1990.  
> **username_0**: @username_1 I apologize for my later in answering to your comment: I am exactly searching for some examples and I'dl like to understand the reason why in these cases the simple interest is used. I further edited my question above in order to precise this point.  
> **username_0**: @username_2 therefore is the use of simple interest simply due to the simplicity of the associated calculations? This seems reasonable.  
> **username_2**: Yes, it’s just a calculation convention, which gives an entirely meaningless answer. Only reason to use it is simplicity. That simplicity was useful before the 1980s, when people were often forced to use tables in books to convert prices to yields, and possibly in things like exams.  
> **username_0**: @username_2 would you like to post your comments as an answer? I am writing a small booklet on the subject and if you do so, I'll be able to cite your comments in the references. Anyway, thank you very much.  

---

## 2 answers

### Answer by username_2 on 2021-02-26. Score: 2 | Accepted answer

Interest payments are contractual payments. They need to be specified with an exact formula. For a given set of cash flows, one could come up with a multitude of formulae that end up giving the same values. In order to make interest rates comparable, laws, regulations, and market conventions specify that different conventions be used.

Of these conventions, simple and compound interest are possible choices. For simple interest, the interest payment is just the interest rate times the principle times a time factor. Compound interest takes into account increases in principal.

If a loan has associated interest payments that must be paid immediately, the loan resembles a generic bond: principal amount does not change. Bonds have a wide variety of conventions to convert the price of a bond to a yield, including a “simple interest rate” convention. However, changing the convention does not change the contractually defined price or cash flows. Since generic bonds do not roll interest payments into the principal, “compound interest” does not make sense.

For loans, interest is often rolled into the principal. We can then use simple interest or compound interest conventions.

Assume a monthly frequency, with no calendar date irregularities, for a loan agreement.

* The interest rate could be specified as a simple interest rate of 1% a month.
* The interest rate could be specified as an annual compound interest of $1.01^{12}-1$ or 12.68% (approx).

Regardless of the convention used, if the borrower makes no payments for a year, the principal will grow by (roughly) 12.68% since the lender will roll the interest into the balance at the end of the month, and then make the simple interest calculation based on the new balance. That is, lenders will still charge interest on interest in practice.

Which one to use is purely a cosmetic decision - is it easier to work with 1% a month, or 12.68% a year?


---

### Answer by username_0 on 2024-01-20. Score: 0

This is just an addition to [username_2 username_2's answer](https://economics.stackexchange.com/a/42772/31887), caused by the fact that recently I stumbled upon the paper [1] by [Eugenio Levi](https://link.springer.com/article/10.1007/s10203-010-0102-y). In the article three conceptions about the concrete meaning of interests laws are analyzed, and in §5, p. 156, where some consideration on interest laws as contracts are offered, the Author states that

> ... la maggior parte dei contratti di prestito prevede l'interesse semplice (se si tratta di operazioni a breve scadenza) o il pagamento periodico degli interessi semplici (se si tratta di operazioni lunga scadenza).  
>   
> *Free Engl. transl.*: ... the majority of loan contracts requires simple interest (in the case of short-term operations) or periodic payment of simple interest (in the case of long-term operations).

Thus it seems that, at least in the fifties of the twentieth century, and at least in Italy (or perhaps in European countries), interests due for loan contracts have been calculated by using simple interests: moreover
following the conception of interest laws as contracts, the author remarks that, in such situations, it is really a matter of taste for such cases to consider simple or compound interest.

**References**

[1] Eugenio Levi, "Sul significato concreto delle leggi di interesse" [free Engl. transl.:"On the concrete meaning of interest laws"] (Italian), in Walter Bigiavi, Gianfranco Cimmino, Paolo Fortunati, Dario Graffi, Antonio Pignedoli, Mario Villa, Giuseppe Varoli (Eds.), *Scritti Matematici in Onore di Filippo Sibirani*, Bologna: Dott. Cesare Zuffi Editore, pp. 151-160 (1957), [Zbl 0077.13406](https://zbmath.org/0077.13406).


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