In this lesson summary review and remind yourself of the key terms and calculations related to the distinction between the real interest rate and the nominal interest rate.
Lesson summary
What you see is what you get, right? Not when it comes to interest rates! When you see an ad saying a bank will pay interest on savings accounts, it doesn’t necessarily mean you will be able to buy 5% more stuff with your money after a year.
When you put in a savings account, the real value of that is what you can buy with it. Therefore the real value of what you earn in interest is what you can buy with that interest. When there is inflation, the purchasing power of the interest you earn decreases. Your real interest is the nominal interest rate (the interest you get paid) minus the rate of inflation (the loss of purchasing power).
Key Terms
| Key term | Definition |
|---|
| nominal interest rate | the interest rate that you earn (or pay) on a loan; this is the amount you see on a sign advertising interest rates. |
| real interest rate | the nominal interest rate adjusted for inflation; this is the effective interest rate that you earn (or pay). |
| Fisher effect | the idea that an increase in expected inflation drives up the nominal interest rate, which leaves the expected real interest rate unchanged |
Key Takeaways
Nominal interest is the sum of the expected real interest rate and the expected inflation rate
How does a bank decide what interest rate to charge? It needs to consider two important things: How much interest is enough to make it worthwhile for the bank to loan the money (the real interest rate they earn)?How much of the interest’s purchasing power might be lost to inflation?
For example, suppose a bank wants to earn interest, but it thinks there will be inflation. If they don’t factor that inflation into what they change in interest, they will effectively earn only (because they will lose of the purchasing power of an interest rate of ). Instead, banks factor inflation into their interest rates. To account for inflation, this bank would charge interest.
Remember from a previous lesson that inflation results in winners and losers? Suppose the bank thought inflation would be , but inflation turned out to be . We can figure out the real interest that the bank actually earned in retrospect:
The bank was hurt by the unexpected inflation because they only got a return of , not the they hoped for. On the other hand, the borrower ended up only paying real interest. The borrower got the better deal!
This is an important takeaway: it was the unanticipated aspect of the inflation that hurt the bank and helped the borrower. If the bank had anticipated the higher rate of inflation, they would have simply charged a higher nominal interest rate to ensure they got the real interest rate.
This is the basic idea behind something called the Fisher Effect. When expected inflation changes, the nominal interest rate will increase. However, inflation will not affect the real interest rate.
Key Equations
The interest rate borrowers pay and savers earn
Sometimes this equation is written using symbols:
Note: sometimes you will see inflation abbreviated using the Greek symbol , and expected inflation abbreviated as .
The real interest rate in retrospect
The actual interest earned (or paid) will depend on the nominal interest rate and how much the inflation rate turned out to be.
For example, the bank expects a real return of to their earnings. They expect the inflation rate to be , so they charge a nominal interest rate of :
However, it turns out that that inflation is 6%. In retrospect they only earned:
In this case, inflation was higher than they anticipated. They actually lost money, rather than earned it.
Common misperceptions
- A point of confusion some people have is whether nominal and real interest rates can be negative. Real interest rates can be negative, but nominal interest rates cannot. Real interest rates are negative when the rate of inflation is higher than the nominal interest rate. Nominal interest rates cannot be negative because if banks charged a negative nominal interest rate, they would be paying you to borrow money! This is called the “zero bound” on interest rates: the nominal interest rate can only go down to .
Discussion questions
Tywin knows he has a debt to repay soon. The bank charges him an interest rate of . If the expected rate of inflation is , how much interest is he effectively paying? Explain.
Calculate the nominal rate of inflation that will be charged if the expected rate of inflation is and the real return desired is . Show all work.
If the rate of inflation is instead, what happens to the value of the money paid back? Explain.
If the actual rate of inflation turns out to be , then the real interest earned from a nominal interest rate of is:
In this case, because the inflation was lower than expected, the real amount paid back () is higher than the real amount that was anticipated (). Lenders benefits from this unanticipated disinflation and borrowers are hurt.
- The real interest rate paid on an asset was , but the nominal rate was . What was the rate of inflation?
FAQs
Nominal interest rate refers to the interest rate before taking inflation into account. Nominal can also refer to the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest.
Is the nominal interest rate the actual rate of interest you earn or pay? ›
Key Terms
| Key term | Definition |
|---|
| nominal interest rate | the interest rate that you earn (or pay) on a loan; this is the amount you see on a sign advertising interest rates. |
| real interest rate | the nominal interest rate adjusted for inflation; this is the effective interest rate that you earn (or pay). |
1 more rowInterest rates represent the cost of borrowing or the return on saving, expressed as a percentage of the total amount of a loan or investment. A nominal interest rate refers to the total of the real interest rate plus a projected rate of inflation.
Is the nominal annual rate is the rate of interest actually paid or earned? ›
Answer and Explanation: The above statement is false. The nominal annual rate is not the actual interest that one pays or earns. This is because the nominal annual interest rate does not take into consideration the inflation rate.
What is an example of a nominal interest rate? ›
The nominal interest rate is often used in banks to describe interest on different loans and in the investment field. For example, if the nominal rate on a loan is 5%, you can expect to pay $50 of interest for $1,000 borrowed. At the year's end, you'll pay $1,050.
What is an example of a nominal rate? ›
Nominal interest rate, r, is an interest rate that does not include any consideration of compounding. By definition, r = interest rate per period x number of periods. e.g. r = 1% per month, or 3% per quarter (three months in a quarter), or 6% per six-month, or 12% per year, or 24% per two-year.
How do you calculate the nominal interest rate? ›
For the principal P of a loan or investment, if interest I is earned in time T, the nominal interest rate is R=I/PT. To earn a real rate of return r if the annual rate of inflation is i, the required nominal rate is approximately R=r+i.
How to calculate nominal rate? ›
Nominal rate of return = Current Investment Value/Original Investment Value – 1. For example, suppose an investor puts $50,000 into a mutual fund. After a year passes, the account grows to a total of $55,000. The current investment value is $55,000, and the original investment value was $50,000.
How to calculate effective interest rate on a loan? ›
The formula and calculations are as follows: Effective annual interest rate = ( 1 + ( nominal rate ÷ number of compounding periods ) ) ^ ( number of compounding periods ) - 1. Investment A = ( 1 + ( 10% ÷ 12 ) ) 12 - 1. Investment B = ( 1 + ( 10.1% ÷ 2 ) ) 2 - 1.
Is nominal interest the same as simple interest? ›
Nominal interest rate is also defined as a stated interest rate. This interest works according to the simple interest and does not take into account the compounding periods.
Nominal and Effective Interest Rates
A statement that the "interest rate is 10%" means that interest is 10% per year, compounded annually. In this case, the nominal annual interest rate is 10%, and the effective annual interest rate is also 10%.
How to calculate real interest rate from nominal interest rate? ›
To calculate a real interest rate, you subtract the inflation rate from the nominal interest rate. In mathematical terms we would phrase it this way: The real interest rate equals the nominal interest rate minus the inflation rate.
Is nominal interest rate monthly or yearly? ›
Nominal versus effective interest rate
The nominal interest rate, also known as an annual percentage rate or APR, is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded).
Can nominal interest rate be negative? ›
A negative interest rate policy (NIRP) is a tool whereby nominal target interest rates are set with a negative value. A negative interest rate environment exists when a central bank or monetary authority sets the nominal overnight interest rate to below zero percent.
How to calculate nominal interest rate compounded monthly? ›
For example: assume you deposit 100 dollars in a bank account and the bank pays you 6% interest compounded monthly. This means the nominal annual interest rate is 6%, interest is compounded each month (12 times per year) with the rate of 6/12 = 0.005 per month, and you receive the interest at the end of each month.
How do you find the nominal interest rate? ›
For the principal P of a loan or investment, if interest I is earned in time T, the nominal interest rate is R=I/PT. To earn a real rate of return r if the annual rate of inflation is i, the required nominal rate is approximately R=r+i.
How do you calculate nominal interest rate? ›
It states that the nominal interest rate is approximately equal to the real interest rate plus the inflation rate (i = R + h). For example, a bond investor is expecting a real interest rate of 5%, when the market shows an expected inflation rate of 3%.
What is a 12% nominal interest rate? ›
The nominal interest rate, also known as an annual percentage rate or APR, is the periodic interest rate multiplied by the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded).
