Defining nominal and real interest rates

Interest rates represent the cost of borrowing money or the return on saving it. They help people and businesses compare the value of money over time, especially when deciding whether to borrow or lend.

Nominal interest rate

The nominal interest rate is the stated rate of interest on a loan or savings account, without any adjustment for changes in purchasing power due to inflation. This rate is what lenders and borrowers agree upon at the start of a loan.

Real interest rate

The real interest rate is the nominal interest rate adjusted for the effects of inflation. It shows the true cost of borrowing or the actual return on savings by accounting for how inflation reduces the value of money over time.

These definitions highlight that nominal rates focus on the face value, while real rates provide a clearer picture of economic impact by considering inflation.

The relationship between nominal rates, real rates, and inflation

Nominal and real interest rates are connected through inflation, which is the general rise in prices over time. This relationship affects decisions made by lenders and borrowers.

How nominal rates are formed

Lenders and borrowers set nominal interest rates based on expectations. The nominal rate combines the expected real interest rate, which is the desired return after inflation, with the expected inflation rate. This occurs because lenders want to protect against losing purchasing power.

Formula for nominal interest rate:

$\text{Nominal interest rate}=\text{expected real interest rate}+\text{expected inflation rate}$

Adjusting for actual inflation to find real rates

Once the loan period ends, the real interest rate can be determined by subtracting the actual inflation rate from the nominal rate. This adjustment reveals whether the lender's return or borrower's cost matched expectations.

Formula for real interest rate:

$\text{Real interest rate}=\text{nominal interest rate}-\text{actual inflation rate}$

Effects of changes in rates and inflation

• If expected inflation rises, nominal rates tend to increase to maintain the real return.
• If actual inflation is higher than expected, the real interest rate falls, benefiting borrowers but hurting lenders.
• If actual inflation is lower than expected, the real interest rate rises, favoring lenders.

This relationship shows how inflation expectations shape borrowing and saving behaviors in the economy.

Worked example - Calculating real interest rate

A borrower takes out a loan at a nominal interest rate of 7%. Over the year, the actual inflation rate turns out to be 3%. Calculate the real interest rate.

Step 1: Identify the values

• Nominal interest rate = 7%
• Actual inflation rate = 3%

Step 2: Apply the real interest rate formula

$\text{Real interest rate}=7\%-3\%$

Step 3: Calculate the real interest rate

$\text{Real interest rate}=4\%$

Step 4: Interpretation

The real cost of borrowing is 4%, meaning the borrower's purchasing power decreases by 4% after accounting for inflation.

Worked example - Calculating nominal interest rate

A lender expects a real interest rate of 2% and anticipates an inflation rate of 4% over the loan period. Calculate the nominal interest rate they would set.

Step 1: Identify the values

• Expected real interest rate = 2%
• Expected inflation rate = 4%

Step 2: Apply the nominal interest rate formula

$\text{Nominal interest rate}=2\%+4\%$

Step 3: Calculate the nominal interest rate

$\text{Nominal interest rate}=6\%$

Step 4: Interpretation

The lender sets a 6% nominal rate to achieve a 2% real return if inflation meets expectations.