Interest is the cost of borrowing capital. It is usually measured with the interest rate, defined as "the amount a lender charges for the use of assets expressed as a percentage of the principal," where the principal denotes the value of loaned assets at the start of the loan.
Interest as a payment is instituted due to time preference: One prefers to have money now rather than in the future, and thus interest becomes one's compensation depending on how much one values the current money in relation to future money. For entrepreneurs and investors, the current money may have an especially high value, as they could utilize it for investments for future income streams. On the loan market, however, the interest rate (or price for borrowing) tends to be set by the supply and demand of loanable funds (i.e. money available to borrow from).
The kind of interest rate described hereto that's solely based upon time preference is called the pure interest rate. Usually, however, other factors also play in, and the interest rate with these included is denoted as the nominal interest rate. Such factors may be inflation or the debtor's risk of default. Younger people may, for instance, have to pay a higher interest rate than many adults, not necessarily because of age discrimination, but because adults tend to have a lengthier credit record to judge from than youngsters, and there are thus more uncertainty as to their likelihood of repaying on time.
Inflation makes an important impact on the interest rate. In addition to the interest rate being set by time preference, one also needs to predict how much the value of the currency will fall during the period of the loan. If one sets it too low, one will likely incur losses; while if one sets it too high in comparison to the current market, one may not find many willing borrowers. In order for statisticians to measure the time preference part of interest, inflation is usually adjusted for, making it the real interest rate.