#### Introduction

When you borrow or lend money, you pay or receive interest. *Compound interest* is paid on the initial capital *and* on accrued past interest.

#### Definitions and basic notions

Interest, from *Concise Encyclopedia of Economics*

Interestis the price people pay for resources now rather than later. Resources, of course, can range from tuition to a big-screen TV. Interest is traditionally expressed as a percentage for a period of one year. If borrowers (those who want resources now) can obtain resources from lenders (those willing to relinquish current control) on the condition that they return 103% of the resources one year later, then the interest rate is by 3%….

Compound Interest, from Thoughtco.com

Compound interest is the interest paid on the initial principal and on the past accumulated interest.

When you borrow money from a bank, you pay interest. Interest is really a fee charged for borrowing money, it is a percentage charged on the principal amount for a period of one year, usually.

If you want to know how much interest you’ll earn on your investment, or if you want to know how much you’ll pay on top of the capital cost of a loan or mortgage, you’ll need to understand how compound interest works.

**Calculate how much you will save:** Formulas and Examples for Calculating Interest on Savings, from TheBalance.com

As you accumulate savings, it helps to learn how to calculate interest. This allows you to plan important goals and understand your progress towards those goals. Calculating the interest you earn is relatively easy, especially if you use free spreadsheets or online calculators….

**Rule of 72**: Economic Growth, *Concise Encyclopedia of Economics*

In the modern version of an old legend, an investment banker asks to be paid by placing a penny on the first square of a chessboard, two pennies on the second square, four on the third, etc. If the banker had requested that only the white squares be used, the initial penny would double in value thirty-one times, leaving $21.5 million on the last square. Using both black and white squares increases the penny to $92 trillion….

you can understand

how long does it take for income to doubledividing the growth rate by the number 72. If growth in the United States continues at the annual rate of 2.1%, per capita income will double every 34 years (72/2.1 = 34). In 102 years, income will be multiplied by eight. This increase is significant, but not unprecedented….

#### In the news and examples

**Lottery payments:** Current value, from *Concise Encyclopedia of Economics*

Present value is the value today of a sum of money in the future. If the appropriate interest rate is 10%, the present value of $100 spent or earned in one year is $100/1.10, or about $91. This simple example illustrates the general truth that the present value of a future amount is less than that actual future amount. If the appropriate interest rate is only 4%, the present value of $100 spent or earned in one year is $100/$1.04, or about $96. This illustrates that the lower the interest rate, the higher the present value. The present value of $100 spent or earned twenty years from now is, using an interest rate of 10%, $100/(1.10)20, or about $15. In other words, the present value of an amount far in the future is a small fraction of the amount….

The concept of present value is very useful. An interesting use is to determine what a lottery prize is really worth. The California state government, for example, announces that one of its lottery prizes is $1 million. But it is not worth the price. Instead, the California government promises to pay $50,000 a year for twenty years. If the discount rate is 10% and the first payment is received immediately, the present value of the lottery prize is only $468,246….

#### A bit of history: primary sources and references

Interest, at Lalor *Cyclopedia of Political Economy*

INTEREST is the product, increase (incrementum), return (reditus) of capital. When the interest represents the sum paid at fixed periods by the borrower to the capital lender, it retains its generic name, or takes the more special designation of annuity or income. The price charged by the owner for the use of land rented by him is the rent. The term income applies more particularly to the product of capital employed in commerce, agriculture or manufactures….

I. INTEREST-BEARING LOANS. Is it allowed to lend at interest? Can one legitimately draw a product from his capital, an income from his money? On this question, which no longer seems to be one, the world, until the end of the last century, was divided. Loans at interest had in their favor the constant practice of peoples, especially of those who distinguished themselves by their progress in wealth, commerce, and industry; on the other, the oracles of religion and the doctors of the law. Now that theology has been humanized on this point and that jurisprudence has relaxed its rigor, socialism has taken up the thesis of the abolition of interest. The sophism has only changed defenders. Instead of justifying this interference with capital by charity or by unenlightened views on morality, one now appeals to envy and lawless passions.

The (so-called) Laws of Moses recognized the legitimacy of lending at interest…

*Defense of attrition*by Jeremy Bentham on Econlib

#### Advanced Resources

*The theory of interest*by Irving Fisher on Econlib

#### Related Topics

Real, relative and nominal prices

Credit

Monetary policy and the Federal Reserve