Mechanics of Interest
When you deposit money into a bank, the bank uses your money to give loans to other customers. In return for the use of your money, the bank pays you interest. Similarly, when you purchase something with a credit card, you pay the credit card company interest for using the money that paid for your purchase. In general, interest is money that a borrower pays a lender for the right to use the money. The interest rate is the percent of the total due that is paid by the borrower to the lender.
The calculation of compound interest is rather simple. To calculate the value of a loan, add one to the interest rate, raise it to the number of years for the loan, and multiply it by the loan amount. For example if you borrow $10,000 at 8% per year, in one year you would owe $10,000 * (1.08 ^ 1) = $800 in interest. To calculate the amount of interest, simply subtract the original loan amount from the total due. In this example, the interest due would be $10,800 - $10,000 = $800.
Reasons for Paying Interest
Why do people pay interest? Lenders demand that borrowers pay interest for several important reasons. First, when people lend money, they can no longer use this money to fund their own purchases. The payment of interest makes up for this inconvenience. Second, a borrower may default on the loan. In this case, the borrower fails to pay back the loan and the lender loses the money, less whatever can be recovered from the borrower. Interest helps to make the risk of default worth taking. In general, the more risk there is of default on the loan, the higher the interest rate demanded by the lender. Finally, and most importantly, lenders demand interest since while the borrower has the money, inflation tends to reduce the real value, or purchasing power, of the loan. In this case, interest allows the balance due to grow as inflation erodes the real value of the balance due.
Real vs. Nominal Interest Rates
We learned above that the third and most important reason why lenders demand interest is that inflation tends to decay the real value of loans over time. For example, let's say a loan is made for $10,000, inflation is 5%, and the loan is paid back after one year. When the loan is made, it can purchase $10,000 worth of goods, such as a compact car. After a year of inflation at 5%, the same compact car costs $10,500. At the same time, one year later, the $10,000 loan is repaid in full. Unfortunately, due to inflation, the real value, or purchasing power, of the money when the loan is repaid is $500 less than when it was made.
By charging an interest rate at least equal to the rate of inflation, this problem is corrected. For example, say a loan is made for $10,000 at 5% interest, inflation is 5%, and the loan is paid back after one year. When the loan is made, it can purchase $10,000 worth of goods, such as a compact car (again). After a year of inflation at 5%, the same compact car costs $10,500. At the same time, one year later, the loan is repaid in full plus interest, totaling $10,500. In this case, the effects of inflation and the interest rate counteract each other so that the real value of the money stays the same even though the nominal value of the money increases by $500.
Two different interest rates are used in the discussion of loans. The nominal interest rate is the interest rate reported when a loan is made. This rate does not take into account the effects of inflation. The real interest rate is not usually reported when a loan is made. This rate takes into account the effects of inflation on the purchasing power of money repaid from a loan.
There is a relationship between the nominal interest rate, the real interest rate, and the rate of inflation. The real interest rate is equal to the nominal interest rate minus the inflation rate; the real interest rate, or the purchasing power of the loan, is equal to the interest earned less the effect of inflation. In the problem above, the nominal interest rate was 5%, the inflation rate was 5%, and thus, using the equation, the real interest rate was 0%. In this case, the lender received no protection from default or payment for the inconvenience of having the money unavailable. In general, lenders always charge a nominal interest rate greater than the expected inflation rate.
The nominal interest rate is what is paid on the balance due on a loan. If the equation presented above is rearranged, we see that the nominal interest rate is equal to the real interest rate plus the inflation rate. In the previous section on the quantity theory of money, we learned that when the Fed increases the money supply, the major effect is an increase in the inflation rate.
From the equation just presented, we learn a second effect of an increase in the money supply. Because the nominal interest rate is equal to the real interest rate plus the inflation rate, an increase in the inflation rate due to an increase in the money supply by the Fed results in an increase in the nominal interest rate. This increase is affected by lenders to ensure that they receive the real interest rate they wanted on the loan, regardless of the effects of inflation. The point for point adjustment of the nominal interest rate to the real interest rate is called the Fischer effect.