Interest Rates

An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for deferring the use of funds and instead lending it to the borrower.

Interests rates are fundamental to a capitalist society. Interest rates are normally expressed as a % rate over the period of one year. Interest rates targets are also a vital tool of monetary policy and are taken into account when dealing with variables like investment, inflation, and unemployment.

Reasons for interest rate change Political short-term gain: Lowering interest rates can give the economy a short-run boost. Under normal conditions, most economists think a cut in interest rates will only give a short term gain in economic activity that will soon be offset by inflation. The quick boost can influence elections. Most economists advocate independent central banks to limit the influence of politics on interest rates. Deferred consumption: When money is loaned the lender delays spending the money on consumption goods. Since according to time preference theory people prefer goods now to goods later, in a free market there will be a positive interest rate. Inflationary expectations: Most economies generally exhibit inflation, meaning a given amount of money buys fewer goods in the future than it will now. The borrower needs to compensate the lender for this.

Reasons for interest rate change… Alternative investments: The lender has a choice between using his money in different investments. If he chooses one, he forgoes the returns from all the others. Different investments effectively compete for funds. Risks of investment: There is always a risk that the borrower will go bankrupt, abscond, die, or otherwise default on the loan. This means that a lender generally charges a risk premium to ensure that, across his investments, he is compensated for those that fail. Liquidity preference: People prefer to have their resources available in a form that can immediately be exchanged, rather than a form that takes time or money to realize. Taxes: Because some of the gains from interest may be subject to taxes, the lender may insist on a higher rate to make up for this loss.

Real vs nominal interest rates The nominal interest rate is the amount, in money terms, of interest payable. For example, suppose a household deposits $100 with a bank for 1 year and they receive interest of $10. At the end of the year their balance is $110. In this case, the nominal Interest rate is 10% per annum. The real interest rate, which measures the purchasing power of interest receipts, is calculated by adjusting the nominal rate charged to take inflation into account.

In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation (in contrast with the real interest rate); or, for interest rates "as stated" without adjustment for the full effect of compounding (also referred to as the nominal annual rate). An interest rate is called nominal if the frequency of compounding (e.g. a month) is not identical to the basic time unit (normally a year).

The nominal interest rate includes both inflation and the real rate of interest. In the case of a loan, this real interest the lender receives as income. If lender is receiving 8 % from a loan and inflation is 8 %, then the real rate of interest is zero because nominal interest and inflation are equal. A lender would have no net benefit from such a loan because inflation fully diminishes the value of the loan's profit. The relationship between real and nominal interest rates can be described in the equation:

where r is the real interest rate, i is the inflation rate, and R is the nominal interest rate. A common approximation for the real interest rate is: real interest rate = nominal interest rate - expected inflation

Nominal vs Effective interest rates The nominal interest rate is the periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding. A nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency and the rate. Although some conventions are used where the compounding frequency is understood, consumers in particular may fail to understand the importance of knowing the effective rate.

Nominal vs Effective interest rates… Nominal interest rates are not comparable unless their compounding periods are the same; effective interest rates correct for this by "converting" nominal rates into annual compound interest. In many cases, depending on local regulations, interest rates as quoted by lenders and in advertisements are based on nominal, not effective interest rates, and hence may understate the interest rate compared to the equivalent effective annual rate. The effective interest rate is always calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective rate, i the nominal rate (as a decimal, e.g. 12% = 0.12), and n the number of compounding periods per year (for example, 12 for monthly compounding):

Nominal vs Effective interest rates… Examples Monthly compounding Example 1: A nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. Example 2: 6% annually is credited as 6%/12 = 0.5% every month. After one year, the initial capital is increased by the factor ( ) 12 ≈ Daily compounding A loan with daily compounding will have a substantially higher rate in effective annual terms. For a loan with a 10% nominal annual rate and daily compounding, the effective annual rate is %. For a loan of $10,000 (paid at the end of the year in a single lump sum), the borrower would pay $51.56 more than one who was charged 10% interest, compounded annually.