Zins

Zins, the German term for interest, is the price paid for the use of money, or the return earned from lending money. The concept is central to loans, deposits, and investments. In everyday usage, Zins is expressed as a percentage rate over a given period, typically annually. The rate can be nominal and may be fixed or variable, and the actual return or cost depends on the compounding method used.

There are two main forms of Zins: simple interest and compound interest. Simple interest is calculated only on the initial principal: interest equals principal times the rate times time. Compound interest is calculated on the initial principal plus accumulated interest, so the amount grows with each compounding period. The accumulated amount after t years is P(1 + r/n)^(nt) when r is the annual rate and n is the number of compounding periods per year.

Zins can be quoted as nominal rates or real rates. The real Zins adjusts for inflation and reflects the true purchasing power of interest earnings or payments. Because inflation reduces value, a higher nominal rate may yield a low or even negative real Zins in inflationary environments.

Common contexts include mortgage loans, savings accounts, bonds, and central bank policy. In many jurisdictions, institutions quote the annual percentage rate (APR) or the annual percentage yield (APY), which account for compounding to varying extents.

See also: interest rate, compound interest, APR, APY, inflation, bond yields.