Interest Rate

An interest rate is the amount of interest charged or paid over a specified period, expressed as a percentage of the principal borrowed, deposited, or invested. For borrowers, it represents a cost of obtaining money; for lenders and depositors, it represents income from supplying funds. Rates are commonly quoted annually. There is no single economy-wide interest rate: banks and financial markets offer different rates for different borrowers, instruments, and maturities. (ecb.europa.eu)

Measurement and compounding

Interest calculations depend on the principal, the rate, the time elapsed, and whether accumulated interest itself earns interest. Under simple interest, interest is calculated only on the principal. Under compound interest, accumulated interest is added to the amount on which subsequent interest is calculated. For example, $1,000 earning 5% annually becomes $1,050 after one year and $1,102.50 after two years if interest is compounded annually and no funds are added or withdrawn. (en.wikipedia.org)

For an unchanged principal $P$, a constant annual rate $i$, and a term of $t$ years, simple interest is $Pit$. If interest is compounded $m$ times each year, the accumulated amount is

The corresponding effective annual interest rate is $(1+i/m)^m-1$. These formulas assume no intervening payments, withdrawals, or fees. Compounding frequency therefore matters when comparing quoted rates. (en.wikipedia.org)

An annual percentage rate (APR) measures borrowing costs more broadly than the contractual interest rate. For United States mortgages, it incorporates interest and certain additional charges, including points and mortgage broker fees. APR is consequently usually higher than the stated interest rate; it is not simply another name for the effective annual rate calculated from compounding alone. (consumerfinance.gov)

Nominal and real rates

A nominal interest rate measures payments in monetary units without adjusting for inflation. A real interest rate adjusts for changes in purchasing power. For a nominal return $i$ and inflation $\pi$ over the same period, the realized real return $r$ satisfies

For relatively small rates, this is approximately $r=i-\pi$. Thus, a positive nominal return can coexist with a negative real return if prices rise faster than the monetary value of the investment. (ecb.europa.eu)

Before a transaction is completed, economists calculate an ex ante real rate using expected inflation; afterward, an ex post rate uses actual inflation. These can differ because future inflation is uncertain. The Fisher equation relates nominal interest, real interest, and expected inflation, explaining why a high nominal rate need not imply a high expected purchasing-power return. (ecb.europa.eu)

Contractual rates and risk

A fixed rate remains unchanged during the period specified in a contract. A floating or variable rate changes according to agreed rules, often using a benchmark plus a contractual margin. An adjustable-rate mortgage, for example, may begin with a fixed introductory rate and subsequently reset at regular intervals. Contracts can impose caps or floors that limit adjustments. (consumerfinance.gov)

Differences between rates reflect more than maturity. Lenders may require compensation for credit risk, including the possibility that a borrower will fail to make promised payments. Funding costs, competition, and conditions in financial markets also influence lending rates. The difference between a lending rate and a benchmark is called a spread, and it can change even when the benchmark remains constant. (rba.gov.au)

Bonds and the term structure

A bond generally promises specified payments over a defined term. Its coupon rate determines contractual interest payments relative to face value, whereas its market yield depends on the price paid and the remaining payments. For a conventional fixed-payment bond, price and yield move in opposite directions: a higher market-required yield reduces the price of its existing payments. (rba.gov.au)

The yield curve, or term structure of interest rates, plots yields against maturity for comparable instruments. It can slope upward, slope downward, or be relatively flat. Its shape reflects expectations about future short-term rates and compensation for holding longer-term instruments. Consequently, a long-term yield is not a pure forecast of future policy rates. Yield curves influence the pricing of fixed-term borrowing and saving products. (rba.gov.au)

Monetary policy and economic activity

A central bank uses interest-rate settings as an instrument of monetary policy. Policy typically operates through a short-term benchmark and influences other rates rather than directly setting every loan or deposit rate. In Australia, for example, the cash rate concerns overnight loans between financial institutions. Other instruments, including asset purchases and guidance about future policy, can influence longer-term rates. (rba.gov.au)

Interest-rate changes affect macroeconomic activity through several channels. Lower rates generally reduce borrowing costs and encourage spending, while higher rates generally restrain demand. Changes also affect borrowers’ repayments, savers’ income, and asset values. International rate differences can influence the exchange rate, altering import prices and export competitiveness. These effects are neither immediate nor mechanically predictable: their timing and magnitude depend on financial conditions and the structure of the economy. (rba.gov.au)