When a borrower (debtor) and a lender (creditor) enter into a contract, the borrower receives funds at the present time from the lender in exchange for paying the funds back at a later time. In essence, the borrower has gained control of the use of money that is owned by the lender. This includes the opportunity to invest this money for the purpose of earning income for the borrower.
The lender is willing to enter into such a contract because income for the lender is involved. The borrower agrees to pay back money in addition to the amount of money borrowed in order to compensate the lender for providing this service. The amount of funds borrowed is called principle. The amount in addition to the principle that the borrower agrees to pay to compensate the lender is called interest.
The amount of the interest, stated as a percentage of the principle and annualized, is called the interest rate. This concept is known as the time value of money.
To the borrower, interest represents a cost of borrowing, called interest expense. To the lender, interest represents income on an investment. The lender is investing funds in the transaction in order to earn income. This is called interest income.
This analysis applies to the bond market as well as such transactions as bank loans, because bonds are actually contracts between lenders and borrowers.
At any given time, different rates of interest will be present for different transactions and different types of transactions. This is because any given interest rate will have at least four different components, which can vary from transaction to transaction (and from situation to situation):
The time value of money: this is the rate of interest that would induce a lender to enter into a transaction in a risk-free environment. This amount would vary with the state of the economy, but would be theoretical in nature, since risk is always involved. It would be equal to the opportunity cost of the transaction.
Risk premium: this is the portion of the interest rate, in addition to the time value of money, that is associated with the risk of default.
Liquidity and marketability: All else equal, a loan that is liquid and marketable would be preferable to a loan that is less liquid or less marketable. A higher interest rate on the less liquid and less marketable loan would compensate for this difference.
Anticipated inflation: A portion of the interest rate is to compensate the lender for the decrease in purchasing power due to inflation during the time that the loan proceeds are outstanding.
The relationship between interest rates and inflation is covered in the Inflation page of this site.