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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 which assumes (more or less explicitly) the use of compound interest, perhaps familiar to all of us, and, en passant, mention the existence of the simple interest. 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.

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    $\begingroup$ 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. $\endgroup$
    – 1muflon1 ♦
    Jan 4, 2021 at 15:08
  • $\begingroup$ @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. $\endgroup$
    – Daniele Tampieri
    Jan 4, 2021 at 15:11
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    $\begingroup$ 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 $\endgroup$
    – 1muflon1 ♦
    Jan 4, 2021 at 15:17
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    $\begingroup$ 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. $\endgroup$
    – Brian Romanchuk
    Jan 4, 2021 at 18:18
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    $\begingroup$ 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. $\endgroup$
    – Brian Romanchuk
    Jan 8, 2021 at 2:48

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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?

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