Interest Rate Definitions

The annual nominal interest rate is the stated interest rate of a given loan. It is the actual monetary price that borrowers pay to lenders to use their money. If the nominal rate on a loan is 5%, then borrowers can expect to pay $5 of interest for every $100 loaned to them for one year.

Simple interest rate is the easiest to calculate as there is no compounding taking place over each year. So, a 5% simple annual interest rate adds 5 percent to the capital sum owed for each year.

If you put a sum of money in the bank and spend the interest earned each year (i.e., the capital stays constant), the amount of money that you will have earned some time in the future is given by the formula:

A=P(1+r)*t

where P is the initial investment (Principal), r is the interest rate per period expressed as a decimal fraction, t is the number of periods, and A is the amount of money in the bank plus the interest you spend at the end of the calculated period.

In compounded interest rates, the rate of annual interest is applied to the principle sum borrowed, plus the additional amount owed in the previous year due to the interest already applied.

If you put a sum of money in the bank and let the interest accumulate, the amount of money that you will have some time in the future is given by the formula:

A=P(1+r)^t

where P is the initial investment, r is the interest rate per period, t is the number of periods, and A is the amount of money in the bank after the periods.

The real interest rate states the “real” rate that the lender receives after inflation is factored in; that is, the interest rate that exceeds the inflation rate. If a bond that compounds annually has a 6% nominal yield and the inflation rate is 4%, then the real rate of interest is only 2%.

The real rate of interest could be said to be the actual mathematical rate at which investors and lenders are profiting from their loans. It is actually possible for real interest rates to be negative if the inflation rate exceeds the nominal rate of an investment. For example, a bond with a 3% nominal rate will have a real interest rate of -1% if the inflation rate is 4%. A comparison of real and nominal interest rates can therefore be summed up in this equation:

Real interest rate = Nominal interest rate – Inflation

Several economic stipulations can be derived from this formula that lenders, borrowers and investors can use to make more informed financial decisions.

Real interest rates can not only be positive or negative, but can also be higher or lower than nominal rates. Nominal interest rates will exceed real rates when the inflation rate is a positive number (as it usually is). But, real rates can also exceed nominal rates during deflation periods.

The effective rate takes the power of compounding into account for Nominal Interest Rate. For example, if a bond pays 6% on an annual basis and compounds semiannually, then an investor who invests $1,000 in this bond will receive $30 of interest after the first 6 months ($1,000 x .03), and $30.90 of interest after the next 6 months ($1,030 x .03). The investor received a total of $60.90 for the year, which means that while the nominal rate was 6%, the effective rate was 6.09%.

Mathematically speaking, the difference between the nominal and effective rates increases with the number of compounding periods within a specific time period.