Fisher Equation

Nominal vs. Real Interest Rate: What is the Difference?

As a quick example, suppose that a loan was issued at a 10.0% nominal interest rate and the expected inflation rate is 6.0%.

Q. Given those assumptions, what is the real interest rate?

If we subtract the inflation rate from the nominal interest rate, the real interest return comes out to 4.0%, which is the yield that the lender is expected to earn from the financing agreement.

But more importantly, the takeaway from our scenario is that even if the lender were to receive all interest payments on time and the original principal on the date of maturity, the actual return is still lower than that of the nominal interest rate due to the effects of inflation.

The risk of inflation is among one of the risks considered by lenders when determining the pricing terms on a debt issuance.

The more concerning matter for lenders is not inflation by itself, but inflation that exceeds their expectations.

On the date that a financing arrangement is finalized, the inflation rate that will occur in the future is an unknown variable. Hence, the lenders in the market (and the borrowers) must use sound judgment to set expectations for future inflation to determine appropriate interest rate pricing.

How the Fisher Effect Impacts Fiscal Policy?

The Fisher Effect describes how the real interest rate and the expected rate of inflation move in tandem.

The practical application here is that if an economy’s actual inflation rate exceeds expectations, the beneficiary is the borrowers at the expense of the lenders.

Thus, unexpected inflation benefits debtors, while reducing the real returns received by creditors.

Given a high interest rate environment, borrowers pay lower real interest rates on their borrowings such as loans and pay them back using less valuable dollars, i.e. the dollar has lost value because of rising inflation.

On the other side, the lenders such as commercial banks earn lower yields in terms of real interest rates. The inflation caused their investments to erode in value, which reduces their real returns.

Fisher Equation Calculator

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Fisher Equation Calculation Example

Suppose a consumer has taken out a loan with an 8.00% fixed interest rate from a commercial bank.

On the initial date of the borrowing, the expected inflation rate was 4.00%.

• Nominal Interest Rate (i) = 8.00%
• Inflation Rate, Expected (πe) = 4.00%

To calculate the estimated real return, we’ll enter our assumptions into the following formula in Excel.

• Real Interest Rate, Estimate = (1 + i) / (1 + πe) – 1
• Real Interest Rate, Estimate (re) = 3.85%

If we used the alternate formula, the expected inflation rate would be 4.00%, reflecting how the difference is relatively marginal.

Next, we’ll assume that the actual inflation data comes out to be 6.00%, meaning that the initial expectations were exceeded by 2.00%.

• Inflation Rate, Actual (πa) = 6.00%

Originally, the lender had expected to earn a real interest rate of around 3.85%. Yet, the higher-than-anticipated inflation rate caused the real interest rate to decline to 1.89%, instead.

• Real Interest Rate, Actual = (1 + i) / (1 + πa) – 1
• Real Interest Rate, Actual = 1.89%
• Actual vs. Estimate Differential = (1.96%)