## Nominal Interest Rate

The nominal interest rate, also known as the annual percentage rate (APR), is the interest rate stated in a loan or investment agreement without considering the effect of compounding or inflation. It is the simple interest rate quoted on loans and investments.

It’s important to distinguish between the nominal interest rate and the real interest rate. The real interest rate adjusts the nominal rate to take into account the impact of inflation, providing a more accurate picture of the cost of borrowing or the return on an investment in terms of purchasing power.

The nominal interest rate also differs from the effective annual rate (EAR), which does account for compounding within a given year. Compounding can occur on various bases—annually, semi-annually, quarterly, monthly, or even daily. The more frequently interest is compounded, the greater the overall interest will be.

For example, if you have a savings account with a nominal interest rate of 5% per year, compounded annually, and you deposit $1,000, you’d have $1,050 after one year. If the interest was compounded semi-annually, however, you would have slightly more than $1,050, because after six months, you would start earning interest on your interest. The nominal rate in both cases is 5%, but the effective annual rate is higher when the interest is compounded more frequently.

## Example of the Nominal Interest Rate

Let’s take a look at an example of a nominal interest rate in the context of a loan:

Suppose you take out a $10,000 loan that has a nominal interest rate of 6% per annum. This 6% is the rate before taking into account compounding or inflation.

If the interest is compounded once per year, the calculation is relatively straightforward. After one year, you would owe:

$10,000 * 0.06 = $600 in interest.

So, your total repayment after one year would be $10,000 + $600 = $10,600.

Now, let’s say that the same loan with a nominal interest rate of 6% is compounded semi-annually. This means interest is calculated twice a year. After the first six months, the interest would be:

$10,000 * 0.06 / 2 = $300

Your loan balance after six months would be $10,000 + $300 = $10,300. The interest for the second six months would then be calculated on this new balance:

$10,300 * 0.06 / 2 = $309

So, your total repayment after one year in this case would be $10,300 + $309 = $10,609.

Even though the nominal interest rate in both cases is 6%, the effective interest rate in the second scenario is slightly higher due to the effects of compounding.

Again, this is a simplified example and does not take into account other factors that might be involved in a real-world loan, such as fees or other charges.