# Relationship between Effective and Nominal rate of interest

14th February 2020

Whether effective and nominal rates can ever be the same depends on whether interest calculations involve simple or compound interest. While in a simple interest calculation effective and nominal rates can be the same, effective and nominal rates will never be the same in a compound interest calculation. Although short-term notes generally use simple interest, the majority of interest is calculated using compound interest. To a small-business owner, this means that except when taking out a short-term note, such as loan to fund working capital, effective and nominal rates can be the same for most every other credit purchase or cash investment.

### Nominal Vs. Effective Rate

Nominal rates are quoted, published or stated rates for loans, credit cards, savings accounts or other short-term investments. Effective rates are what borrowers or investors actually pay or receive, depending on whether or how frequently interest is compounded. When interest is calculated and added only once, such as in a simple interest calculation, the nominal rate and effective interest rates are equal. With compounding, a calculation in which interest is charged on the loan or investment principal plus any accrued interest up to the point at which interest is being calculated, however, the difference between nominal and effective increases exponentially according to the number of compounding periods. Compounding can take place daily, monthly, quarterly or semi-annually, depending on the account and financial institution regulations.

### Simple Interest

The formula for calculating simple interest is “P x I x T” or principle multiplied by the interest rate per period multiplied by the time the money is being borrowed or invested. This formula illustrates that because interest is always being calculated on the principal amount, regardless of the time period involved, the nominal and effective rates will always be equal . If a small-business owner takes out a \$5,000 simple interest loan at a nominal rate of 10 percent, \$500 of interest will be added to the loan will each year, regardless of the number of years. To illustrate, just as \$5,000 x 0.10 x 1 equals \$500, \$5,000 x 0.10 x 5 equals \$2,500 or \$500 per year. The nominal and effective rates of 10 percent in both calculations are equal.

### Compound Interest

The formula for calculating compound interest shows how nominal and effective rates will never be equal. The formula is “P x (1 + i)n – P” where “n” is the number of compounding periods. In a compound interest calculation, the only time interest is charged or added to the principal is in the first compounding period. The base for each subsequent compounding period is the principal plus any accrued interest. If a small-business owner takes out a one-year \$5,000 compound-interest loan at a nominal interest rate of 10 percent, where interest is compounded monthly, total interest that accumulates over the year is \$5,000 x (1 + .10)5 – \$5,000 or \$550. The nominal rate of 10 percent and the effective rate of 11 percent clearly aren’t the same.

### Effect On Small Business Owners

It’s crucial that whether the intent is to borrow or invest, small-business owners pay close attention to effective and nominal rates as well as the number of compounding periods. Compounding interest not only creates distance between nominal and effective rates but also works in favor of lenders. For example, a bank, credit card company or auto dealership might advertise a low nominal rate, but compound interest monthly. This in effect significantly increases the total amount owed. This is one reason why lenders advertise or quote nominal rather than effective rates in lending situations.