The rate of interest measures the percentage reward a lender receives for deferring the consumption of resources until a future date. Correspondingly, it measures the price a borrower pays to have resources now.

Suppose I have \$100 today that I am willing to lend for one year at an annual interest rate of 5 percent. At the end of the year, I get back my \$100 plus \$5 interest (0.05 × 100), for a total of \$105. The general relationship is:

Money Today (1 + interest rate) = Money Next Year

We can also ask a different question: What is the most I would pay today to get \$105 next year? If the rate of interest is 5 percent, the most I would pay is \$100. I would not pay \$101, because if I had \$101 and invested it at 5 percent, I would have \$106 next year. Thus, we say that the value of money in the future should be discounted, and \$100 is the “discounted present value” of \$105 next year. The general relationship is:

 Money Today = Money Next Year (1 + interest rate)

The higher the interest rate, the more valuable is money today and the lower is the present value of money in the future.

Now, suppose I am willing to lend my money out for a second year. I lend out \$105, the amount I have next year, at 5 percent and have \$110.25 at the end of year two. Note that I have earned an extra \$5.25 in the second year because the interest that I earned in year one also earns interest in year two. This is what we mean by the term “compound interest”—the interest that money earns also earns interest. Albert Einstein is reported to have said that compound interest is the greatest force in the world. Money left in interest-bearing investments can compound to extremely large sums.

A simple rule, the rule of 72, tells how long it takes your money to double if it is invested at compound interest. The number 72 divided by the interest rate gives the approximate number of years it will take to double your money. For example, at a 5 percent interest rate, it takes about fourteen years to double your money (72 ÷ 5 = 14.4), while at an interest rate of 10 percent, it takes about seven years.

There is a wonderful actual example of the power of compound interest. Upon his death in 1791, Benjamin Franklin left \$5,000 to each of his favorite cities, Boston and Philadelphia. He stipulated that the money should be invested and not paid out for one hundred to two hundred years. At one hundred years, each city could withdraw \$500,000; after two hundred years, they could withdraw the remainder. They did withdraw \$500,000 in 1891; they invested the remainder and, in 1991, each city received approximately \$20,000,000.

What determines the magnitude of the interest rate in an economy? Let us consider five of the most important factors.

1. The strength of the economy and the willingness to save. Interest rates are determined in a free market where supply and demand interact. The supply of funds is influenced by the willingness of consumers, businesses, and governments to save. The demand for funds reflects the desires of businesses, households, and governments to spend more than they take in as revenues. Usually, in very strong economic expansions, businesses’ desire to invest in plants and equipment and individuals’ desire to invest in housing tend to drive interest rates up. During periods of weak economic conditions, business and housing investment falls and interest rates tend to decline. Such declines are often reinforced by the policies of the country’s central bank (the Federal Reserve in the United States), which attempts to reduce interest rates in order to stimulate housing and other interest-sensitive investments.

2. The rate of inflation. People’s willingness to lend money depends partly on the inflation rate. If prices are expected to be stable, I may be happy to lend money for a year at 4 percent because I expect to have 4 percent more purchasing power at the end of the year. But suppose the inflation rate is expected to be 10 percent. Then, all other things being equal, I will insist on a 14 percent rate on interest, ten percentage points of which compensate me for the inflation.1 Economist irving fisher pointed out this fact almost a century ago, distinguishing clearly between the real rate of interest (4 percent in the above example) and the nominal rate of interest (14 percent in the above example), which equals the real rate plus the expected inflation rate.

3. The riskiness of the borrower. I am willing to lend money to my government or to my local bank (whose deposits are generally guaranteed by the government) at a lower rate than I would lend to my wastrel nephew or to my cousin’s risky new venture. The greater the risk that my loan will not be paid back in full, the larger is the interest rate I will demand to compensate me for that risk. Thus, there is a risk structure to interest rates. The greater the risk that the borrower will not repay in full, the greater is the rate of interest.

4. The tax treatment of the interest. In most cases, the interest I receive from lending money is fully taxable. In certain cases, however, the interest is tax free. If I lend to my local or state government, the interest on my loan is free of both federal and state taxes. Hence, I am willing to accept a lower rate of interest on loans that have favorable tax treatment.

5. The time period of the loan. In general, lenders demand a higher rate of interest for loans of longer maturity. The interest rate on a ten-year loan is usually higher than that on a one-year loan, and the rate I can get on a three-year bank certificate of deposit is generally higher than the rate on a six-month certificate of deposit. But this relationship does not always hold; to understand the reasons, it is necessary to understand the basics of bond investing.

Most long-term loans are made via bond instruments. A bond is simply a long-term IOU issued by a government, a corporation, or some other entity. When you invest in a bond, you are lending money to the issuer. The interest payments on the bond are often referred to as “coupon” payments because up through the 1950s, most bond investors actually clipped interest coupons from the bonds and presented them to their banks for payment. (By 1980 bonds with actual coupons had virtually disappeared.) The coupon payment is fixed for the life of the bond. Thus, if a one-thousand-dollar twenty-year bond has a fifty-dollar-per-year interest (coupon) payment, that payment never changes. But, as indicated above, interest rates do change from year to year in response to changes in economic conditions, inflation, monetary policy, and so on. The price of the bond is simply the discounted present value of the fixed interest payments and of the face value of the loan payable at maturity. Now, if interest rates rise (the discount factor is higher), then the present value, or price, of the bond will fall. This leads to three basic facts facing the bond investor:

1.

If interest rates rise, bond prices fall.

2.

If interest rates fall, bond prices rise.

3.

The longer the period to maturity of the bond, the greater is the potential fluctuation in price when interest rates change.

If you hold a bond to maturity, you need not worry if the price bounces around in the interim. But if you have to sell prior to maturity, you may receive less than you paid for the bond. The longer the maturity of the bond, the greater is the risk of loss because long-term bond prices are more volatile than shorter-term issues. To compensate for that risk of price fluctuation, longer-term bonds usually have higher interest rates than shorter-term issues. This tendency of long rates to exceed short rates is called the risk-premium theory of the yield structure. This relationship between interest rates for loans or bonds and various terms to maturity is often depicted in a graph showing interest rates on the vertical axis and term to maturity on the horizontal. The general shape of that graph is called the shape of the yield curve, and typically the curve is rising. In other words, the longer term the bond, the greater is the interest rate. This typical shape reflects the risk premium for holding longer-term debt.

Long-term rates are not always higher than short-term rates, however. Expectations also influence the shape of the yield curve. Suppose, for example, that the economy has been booming and the central bank, in response, chooses a restrictive monetary policy that drives up interest rates. To implement such a policy, central banks sell short-term bonds, pushing their prices down and interest rates up. Interest rates, short term and long term, tend to rise together. But if bond investors believe such a restrictive policy is likely to be temporary, they may expect interest rates to fall in the future. In such an event, bond prices can be expected to rise, giving bondholders a capital gain. Thus long-term bonds may be particularly attractive during periods of unusually high short-term interest rates, and in bidding for these long-term bonds, investors drive their prices up and their yields down. The result is a flattening, and sometimes even an inversion, in the yield curve. Indeed, there were periods during the 1980s when U.S. Treasury securities yielded 10 percent or more and long-term interest rates (yields) were well below shorter-term rates.

Expectations can also influence the yield curve in the opposite direction, making it steeper than is typical. This can happen when interest rates are unusually low, as they were in the United States in the early 2000s. In such a case, investors will expect interest rates to rise in the future, causing large capital losses to holders of long-term bonds. This would cause investors to sell long-term bonds until the prices came down enough to give them higher yields, thus compensating them for the expected capital loss. The result is long-term rates that exceed short-term rates by more than the “normal” amount.

In sum, the term structure of interest rates—or, equivalently, the shape of the yield curve—is likely to be influenced both by investors’ risk preferences and by their expectations of future interest rates.

Burton G. Malkiel, the Chemical Bank Chairman’s Professor of Economics at Princeton University, is the author of the widely read investment book A Random Walk down Wall Street. He was previously dean of the Yale School of Management and William S. Beinecke Professor of Management Studies there. He is also a past member of the Council of Economic Advisers and a past president of the American Finance Association.

Fabozzi, Frank J. Bond Markets, Analysis and Strategies. 4th ed. New York: Prentice Hall, 2000.
Fisher, Irving. The Theory of Interest. 1930. Reprint. Brookfield, Vt.: Pickering and Chatto, 1997. Available online at: http://www.econlib.org/library/YPDBooks/Fisher/fshToI.html
Patinkin, Don. “Interest.” In International Encyclopedia of the Social Sciences. Vol. 7. New York: Macmillan, 1968.

## Footnotes

Actually, I will insist on 14.4 percent, 4 percent to compensate me for the inflation-caused loss of principal and 0.4 percent to compensate me for the inflation-caused loss of real interest. The general relationship is given by the mathematical formula: 1 + i = (1 + r) × (1 + p), where i is the nominal interest rate (the one we observe), r is the real interest rate (the one that would exist if inflation were expected to be zero), and p is the expected inflation rate.