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## What Is Nominal Interest Rate?

The nominal interest rate is the advertised interest rate of an interest-bearing account. For instance, if a bank promotes a savings account that pays a 4% rate of interest—either annually or in shorter compounding periods—that 4% is the nominal interest rate. But this does not mean that if you park your money into that account, you’ll have 4% more purchasing power at the end of an interest cycle.

Why is this? Because the nominal interest rate also includes the overall inflation rate, and that inflation rate affects the whole economy, not just that bank’s savings account. To isolate the interest that is tied to that specific account, we must calculate what’s called the **real interest rate**.

## Who Controls the Nominal Interest Rate?

Central banks, such as the United States Federal Reserve, set short-term nominal interest rates. This is their primary mechanism for affecting monetary policy. The short-term nominal interest rate represents that rate at which central banks lend money to smaller banks, who in turn lend money to consumers at higher rates (which is how they make their profit).

When the nominal interest rate is low, investment traditionally increases because borrowers have less to pay in interest. For instance, in the aftermath of the financial crisis and Great Recession in 2008, the Federal Reserve set its nominal rate (known as the Federal Funds Rate) to nearly zero percent — a rate that was designed to spur investment and boost the gross domestic product.

Learn more about How ‘08 Happened here.

## What Is the Formula for Nominal Interest Rates?

The difference between real and nominal interest rates can be represented using the Fisher Equation.

It begins as: *i* ≈ *r* + π, where *i* is the nominal interest rate, *r* is the real interest rate, and π is the rate of inflation.

Economists manipulate this equation to read: 1+*i* = (1+*r*)(1+π)

It requires a multi-step mathematical process to derive one of these equations from the other, but both undoubtedly represent the relationship between a real interest rate, a nominal interest rate, and the rate of inflation.

When predicting future economic growth, economists will often replace the rate of inflation with the expected rate of inflation (represented with the subscript e). The inflation expectations of economists and bankers are not always accurate, and so there is always some risk in assuming a future rate of inflation.

This leads to the Fisher Effect, which consists of two assertions:

1. An increase in expected inflation will drive up the nominal interest rate

2. Accounting for such inflation leaves the expected real percentage rate unchanged

## Nominal Interest Rate vs. Real Interest Rate

The real interest rate is the rate of interest paid to an investor, minus inflation. Natural inflation in the economy will affect *all* interest-bearing accounts, not just the one you see an add for. Let’s say, for instance, that you invest your money in the aforementioned savings account that promises a 4% rate of return. But let’s also say that the inflation rate is 3%. This means that the real interest rate of the account is actually 1%, not 4%.

This means that if you placed 100 dollars into such a savings account, you would receive four dollars at the end of your first interest cycle (the amount generated by your four percent interest rate). One of those dollars could be traced to the real interest rate of the account, and the remaining three dollars could be accounted for by inflation.

## Nominal Interest Rate vs. Effective Interest Rate

Nominal interest rates can be difficult to compare because compound interest depends on the length of each compounding period. Here’s how this works in real terms:

- Let’s say you are trying to choose between two interest-bearing accounts that both offer a nominal interest rate of 10%. The first account compounds annually (once per year), while the second account compounds quarterly (four times per year).
- If you put $100 into the first account, it will pay $10 in interest by the end of the year. This is because it has one compounding period per year, and it guarantees a 10 percent rate of interest during that period.
- If you put $100 into the second account, it will pay $46.41 in interest by the end of the year. Why? Because of its greater number of periods in a calendar year. The second account compounds four times over the course of the year, and every time it does, it pays 10 percent of the amount in your account.

Both of these hypothetical accounts claim to offer a 10% nominal interest, but one yields a much higher real return than the other. Fortunately there is a tool to quickly compare the two accounts without requiring the customer to do a bunch of math. That tool is the **effective annual interest rate**.

The effective annual interest rate represents a nominal interest rate as an annual compound interest rate. This eliminates the confusion about the number of periods connected to an advertised nominal interest rate. The truth is that banks could deceive customers by advertising accounts with higher rates but very long compounding periods. Despite the high advertised rates, because it takes so long for the interest to compound, the real rate of those accounts may be nothing special.

So to find the real value of an interest bearing account, look for its effective rate. This is sometimes called the EIR (for effective interest rate) or AER (for annual equivalent rate). Note that these are slightly different from an APR (annual percentage rate) because an APR doesn’t factor in the effects of compounding.

Comparing investment accounts can be intimidating. But by understanding the difference between a nominal rate, a real rate, and an effective rate, consumers can make informed choices and thus choose an account with an *actual* rate that is worthy of investment.

Learn more about economics and society with Paul Krugman here.