I am currently working in the lending business. We charge borrower interest. Recently, I am tasked to work on PnL, and interest loss. But I have little understandings on interest. Why is there an interest? What is interest? How does it determined? The questions came into my mind when I am doing another search on how the “rate” formula in Excel calculates the EIR (effective interest rate). I will save this to another article because I think the topic on interest is much more interesting.

I know there is a famous book called *The Theory of Interest* written by I. Fisher. But I found a shorter version written before the famous book and by the same author: THE INPATIENCE THEORY OF INTEREST A STUDY OF THE CAUSES DETERMINING THE RATE OF INTEREST. You can find the free copy Here.

The book starts with a definition of interest, then reviews some previous theories on interest, and finally proposes a so called “impatience theory of interest”.

The definition of interest is easy to understand since we experienced it in our daily life. It is the price charged on capital. It is the price paid for this year’s money in terms of next year’s money. Interest can be more subtle compared with borrowing money since the price of good at present is the discounted future utility.

I. Fisher briefly discusses a few theories of interest and their pitfalls. I do not fully understand all of them. I will just list some points which I found interesting. First of all, **the rate of interest depends on the amount of money in circulation**. This is wrong. Plentiful of money not only raise the supply of money but also the demand of money because more money will increase price and borrower would therefore need to borrow more money in order to purchase the same amount of goods. Secondly, **interest is due to productivity of capital**. For example, if I invest 5,000 dollars into a bond, it may generate 10% interest, which is 500 dollars. So the capital yields 10% income. This is also problematic. Why the bond worth 5,000 at the first place? It is because it discounted the future income into present value. That discounted rate is 10%. We get out what we put in in the equation.

Having reviewed previous theories, the author proposes his own theory: **Human Impatience Is the True Basis of Interest**. As long as people like to have things today rather than tomorrow, there will be a rate of interest. Interest is impatience crystallized into a market price. It can be expressed in numbers as the premium that a man is willing to pay for this year’s money over next year’s money.

The author listed several factors affecting the so called impatience, including foresight, self-control, habit, expectation of life, love for posterity, and expected income. Although I may be a naive student, I think the main reason human is impatient is because life is short, or in other words, time is limited. And our expectation on current and future income will also greatly affect the level of impatience. If the expected income is increasing, this will make people impatience because you can spend the excess income in the future now.

Although the rate of impatience is different between individuals, it will stabilize into a market rate based on supply and demand provided with some assumptions, including the absence of risk, a fore known income stream, and people are free to exchange their present and future income. For any particular individual, if the rate of impatience is above the market rate, he will sell some of the future income (I.e. borrow) in exchange for present income. If the rate of impatience is below the market rate, he will sell some of the present income (I.e. lend) in exchange for future income.

This concludes the short summary on the theory of interest. But there are many more unknowns to be answers. I am thinking, why there is negative interest rate? Why the interest rate is different between countries? Why the governments/ central banks can set the interest rates? But anyways, at least, I know interest is a price on impatience.