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.
