Nominal Interest Rate

The nominal interest rate can refer to two values. First, it represents an interest rate that does not consider inflation or compounding. Depending on the context, the formulas and functionalities of this value vary.

In economics, this rate contrasts with the real interest rate. Both measure a rate of return on borrowed money, but how this value is calculated differs. The nominal value is typically the number that is displayed or advertised.

For example, a bank may lend you at 6% annual interest. In this situation, 6% is the nominal interest rate. However, the real interest rate reflects the change in the purchasing power of your money.

Although your bank balance may have grown from $1,000 to $1,060 throughout the year, how much you can purchase with the new balance may also differ. For example, if the inflation rate was 3%, a good that previously would cost $100 may now cost $103. 

Let’s evaluate this change on the amount that you can buy. In the starting state, you could have purchased ten units of this product ($1000/$100). Instead, you can purchase around 10.29 units ($1060/103).

If inflation did not occur, you should have been able to purchase 10.6 units of the product. However, your purchasing power has been eroded, leaving you with a modest increase of 2.9%. 

This statement still holds when you assume that the value refers to finance. In this situation, the value exists in contrast to the effective interest rate, which is a value that incorporates the compounding effects of interest.

Because the nominal value does not compound, it is only equivalent to the effective interest rate when the compounding period is a year. As a result, this creates some issues when comparing different interest rates.

For example, how would you compare a loan that charges 8% compounded quarterly with another that charges 7% compounded monthly? Then, you need to convert these values into effective interest rates to evaluate which is better.

The effective interest rate refers to a value equivalent to the interest after it is compounded. It combines the complexity of multiple compounding periods into a single interest rate applied once.

For example, take a special interest rate compounded quarterly with an effective interest rate of 8.5%. The rate simply means that the resulting interest is 8.5% of the original principal after compounding four times.

Effective interest rates can be compared easily by removing the number of compounding periods. 

How does the Nominal Interest Rate work?

The nominal interest rate for many loans is a value that is largely influenced by the Federal Reserve’s federal funds rate, which is the rate at which banks charge each other for overnight loans. 

Although this form of borrowing is extremely short-term, the target rate can have many further effects. Other interest rates often track this value indirectly, including long-term rates.

The Federal Open Market Committee sets the federal funds rate. This target can affect the supply and demand for money, although this is designed for bank-to-bank loans.

For example, if the FOMC decides to raise the federal funds rate to curb inflation, banks now face higher interest rates whenever they need to get an overnight loan. As a result, banks also charge people higher interest rates.

When interest rates rise, we borrow less because the cost of borrowing money is greater. Instead, more may choose to save, profiting from the high interest. However, this will have repercussions for the general economy.

Increased interest rates have a similar effect on businesses. Companies that decide to expand or engage in a costly project often turn to lenders for funding. However, the business may delay the investment if it borrows a lot.

In addition, as people save more of their income, aggregate consumption in the economy decreases, which can cool down a heated economy. It becomes clearer why this occurs if you examine the intertemporal substitution within households.

Let's imagine the going interest rate is 5%, and a family with an income of $80,000 is deciding how to budget this money. In this case, they could have $84,000 after a year if they decided to save the entire amount. However, perhaps they decide only to save $40,000 instead so that they can eat in the first year.

Now let’s consider if the interest rate was, unfathomably, 40% a year. If the same family saved the entire amount, they would have $112,000 the next year. 

Faced with this decision, the family would likely minimize spending in the first year. The increased savings would allow them to reap the rewards in the second year.

In economic terms, they postponed their consumption of goods and services today when the consumption cost is high. In doing so, they can consume more tomorrow.

By earning interest, they can produce more benefits in the future than if the money was spent today.

On a national scale, heightened interest rates would reduce spending nationwide while boosting savings. As a result, the FOMC can lower the federal funds rate, a nominal interest rate, to cool down the economy.

The FOMC tends to keep interest rates high during expansions and low during recessions to ensure stability. However, these changes can also shape other aspects of the economy, like consumer optimism.

How to calculate the Nominal Interest Rate?

The formulas will vary Depending on the nominal interest rate in question. 

To find the value in regards to inflation, use the Fisher equation:

(1 + i) = (1 + r)(1 + 𝝅)

Where:

• i stands for the nominal interest rate
• r stands for the real interest rate
• 𝝅 stands for the rate of inflation

In most cases, however, the previous formula can be simplified because i and r are so small that their product becomes negligible. We end up with the following approximation:

i = r + 𝝅

To find the nominal interest rate; therefore, you only need the values of the real interest rate and inflation values. 

One method of determining this value takes advantage of the defining characteristic of Treasury Inflation Protected Securities (TIPS)—that they are indexed to inflation. 

This technique requires finding the difference between the yield of Treasury bonds and TIPS of the same maturity. This works because TIPS adapts to inflation and will pay out an inflation-adjusted principal. 

As a result, the TIPS yield includes the expected inflation rate.

Now, let’s shift gears to discussing the formula for finding the other nominal interest rate. Again, this value can be calculated from the effective interest rate and the number of compounding periods.

n = m × [ ( 1 + e)^1/m - 1 ]

Where:

• n is the nominal interest rate
• m is the number of compounding periods
• e is the effective interest rate

Conversely, the effective interest rate can be calculated by the following formula:

e = (1 + n/m)^m - 1

Let’s return to our original example. When comparing 8% interest compounded quarterly with 7% interest compounded monthly, we can convert these nominal rates into effective interest rates.

Starting with the 8% compounded quarterly, because it compounds four times a year, m, in this case, is four.

8.24% = (1 + 0.08/4)⁴ - 1

Let’s compare this to 7% interest compounded twelve times a year.

7.23% = (1 + 0.07/12)¹² - 1

As shown, the effective interest is greater in the loan, with 8% interest compounded quarterly even though it had fewer compounding periods.

Nominal Interest Rate Examples

Let’s consider the example of someone purchasing a new car. To finance this purchase, she goes to her bank and requests a loan of $30,000. However, after reviewing her credit history, the bank only allotted her a maximum loan of $25,000.

In addition, because of her previous failure to pay her rent on time, they charged her a nominal interest rate of 6.5%, compounded monthly. For simplicity, let’s assume that she makes one payment per year after interest has compounded for twelve months.

At the end of the first year, she would need to pay part of the loan and the effective interest rate of 6.70%.

6.70% = (1 + 0.065/12)¹² - 1

Let’s consider what would happen when we incorporate inflation into the calculations.

1. Without changing anything from the previous formula, 6.70% of $25,000 is $1,675. This creates a total of $26,675 by the end of year one. 
2. What if inflation ran rampant that year, reaching record levels of 35%? This would decrease the purchasing power of the same $26,675 even though the nominal value hasn’t changed because the same $26,675 is worth less than a year ago.
3. Even though the face value of the loan stayed constant, the intrinsic value of the loan fell. This benefits our example customer because the loan would be easier to pay off if her wages kept up with inflation.

How about the opposite? What if deflation occurred at the same rate? All else was kept the same; this would make the loan more burdensome. Each dollar of the $26,675 carries a little more weight, making the entire loan more expensive to pay off.

To illustrate this, imagine if deflation occurred so heavily that you could purchase a new phone for $50. The $26,675 would be an outrageous amount to pay! As a result, unexpected deflation harms the borrower.

In general, when setting interest rates, lenders will have set expectations of inflation that will be incorporated into the calculations. 

For example, if a particular lender believes that inflation will be 5% this year and wants to receive 3% in interest, they will charge an 8% nominal interest rate. However, unexpected inflation can throw these calculations off.

As illustrated, the nominal interest rate is a subjective number value that depends on the purchasing power of money. 

Although the bank set the interest rate for our example customer at 6.5%, the real interest rate is more important to the borrower because the value of money can change. This is why it is crucial to examine nominal values closely. 

High expectations for inflation may cause high nominal interest rates.

Researched and Authored by Haimeng Yang | LinkedIn

Reviewed and Edited by Basil Khalidi | LinkedIn

Free resources

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• Federal Discount Rate
• Federal Funds Rate
• Federal Income Tax
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• Yield Curve