# Compound Interest

#### Introduction

#### Definitions and Basics

Interest, from the *Concise Encyclopedia of Economics*

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

Compound Interest, from About.com

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

Compound interestis paid on the original principalandon the accumulated past interest….If you borrow for 5 years the

formulawill look like A=P(1+r)^{5}….

Calculate how much you’ll save:

Compound Interest Calculator, from About.com

The compound interest calculator is intended to show you how much you’ll have saved after a given number of years. You’ll know how much of your final balance is due to interest earnings, and you can use the compound interest calculator to see how different interest rates affect the outcome….

**Rule of 72**:

EconomicGrowth, from the *Concise Encyclopedia of Economics*

In the modern version of an old legend, an investment banker asks to be paid by placing one penny on the first square of a chess board, two pennies on the second square, four on the third, etc. If the banker had asked 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 the black and the white squares makes the penny grow to $92,000,000 billion….

You can figure out

how long it takes income to doubleby dividing the growth rate into the number 72. If growth in the United States continues at the annual rate of 2.1 percent, income per capita will double every 34 years (72/2.1 = 34). In 102 years, income will increase eightfold. This increase is large, but not unprecedented….

#### In the News and Examples

Lottery payments:

Present Value, from the *Concise Encyclopedia of Economics*

Present value is the value today of an amount of money in the future. If the appropriate interest rate is 10 percent, then the present value of $100 spent or earned one year from now is $100/1.10, which is 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 percent, then the present value of $100 spent or earned one year from now is $100/1.04, or about $96. This illustrates the fact 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 percent, $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. One interesting use is to determine what a lottery prize is really worth. The California state government, for example, advertises that one of its lottery prizes is $1 million. But that is not the value of the prize. Instead, the California government promises to pay $50,000 a year for twenty years. If the discount rate is 10 percent and the first payment is received immediately, then the present value of the lottery prize is only $468,246….

#### A Little History: Primary Sources and References

Interest, in Lalor’s *Cyclopedia of Political Economy*

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

I. LOANS AT INTEREST. Is it permissible to loan at interest? Can one legitimately derive a product from his capital, a revenue from his money? On this question, which no longer seems to be one, the world, until toward the latter part of the last century, was divided. Loans at interest had in their favor the constant practice of peoples, especially of those noted for their progress in wealth, commerce and industry; on the other side were the oracles of religion and the doctors of the law. Now that theology has become more humane on this point, and 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 on the ground of charity or in consequence of unenlightened views in regard to morality, appeal is now made to envy and the anarchical passions.

The (so-called) laws of Moses recognized the legitimacy of loaning at interest…

*Defence of Usury*, by Jeremy Bentham on Econlib

#### Advanced Resources

*The Theory of Interest*, by Irving Fisher on Econlib

#### Related Topics

Real, Relative, and Nominal Prices

Monetary Policy and the Federal Reserve