# Interest Rates

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By , reviewed by Tom McKenzie

Readers are probably familiar with the concept of interest rates in the world of everyday finance. Savings accounts, student loans, mortgages, etc. are all accompanied by an interest rate that partly determines how much money is added to a savings account or to the amount of debt someone owes.

Interest rates in general economics are (for once) essentially the same thing as they are in finance: a percentage that determines how much a financial balance will grow with each predefined period of time. Nevertheless, interest rates are a very important linchpin of macroeconomics and have far-reaching consequences for the economy. Before describing why this is, it helps to clearly define what interest rates are in economics.

As a side note, inflation happens to be very important when learning about interest rates. Itâ€™s a good idea to be comfortable with the concept before learning more fully about interest rates.

## Nominal vs. real interest rates: whatâ€™s the difference?

In the real world, the cost of borrowing is denoted in terms of the (nominal) interest rate. But there are actually two interest rates that exist simultaneously: nominal interest rates and real interest rates. The nominal rate is the rate that we always deal with in the real world. Interest rates that are listed on savings accounts, mortgages, other types of loans, etc. are nominal interest rates. They are used to calculate interest payments and other quantities that factor in the rate of interest.

Real interest rates, though, are â€śhiddenâ€ť interest rates that people are actually paying instead of the nominal rates they agreed to! But rather than being the result of some crazy conspiracy, real interest rates exist because of inflation. When there is inflation, money loses its purchasing power over time. The same amount of cash can purchase fewer goods and services in the future. This means that nominal interest rates donâ€™t tell the full story of a financial agreement.

For example, suppose that you take out a loan of $100 that must be paid back with interest in one year. The nominal interest rate that you agree to is 5% â€“ that is, when the debt comes due, you must pay back$105, which is an extra $5 on top of the original amount. If there is no inflation, the real interest rate is also 5% in this case. But, suppose that inflation is currently 1% per year. This means that one year later when your debt comes due, you still owe$105, but the purchasing power of that money has changed over the life of the loan. The inflation has eroded the value of $105 so that it can buy fewer things than it could the year prior â€“ specifically, it can purchase 1% fewer goods or services than it could before. Because of this inflation, when you pay back the$105, youâ€™re actually paying an interest rate of only 4% â€“ the agreed-upon 5% interest minus the amount of inflation, which was 1%. Therefore, in this case the real interest rate â€“ the one that accounts for the effect of inflation on the purchasing power of money â€“ was only 4%. But when you signed the loan, neither you nor the loan servicer could know that inflation would be 1%, so it was difficult to account for when making the agreement.

Therefore, the real interest rate has a simple formula that we can write down mathematically: r = i â€“ đťś‹, where r is the real interest rate, i is the nominal rate, and đťś‹ is the inflation rate. Note that itâ€™s technically possible for the real rate of interest to be negative if inflation is higher than the nominal rate.

## Winners and losers when real interest rates differ due to inflation

The above example was relatively innocuous, but it should quickly become evident that large changes in inflation can cause serious problems for these types of financial agreements. As a quick summary, letâ€™s consider who â€świnsâ€ť and who â€ślosesâ€ť when high inflation causes the real rate of interest to be less than the nominal rate, like it was in our example.

Clearly, an economic agent who takes on debt wins when the real interest rate is lower than the agreed-upon nominal interest rate. In this case, they end up paying back less than the agreed-upon amount in terms of real purchasing power. Conversely, the lender â€ślosesâ€ť, as they receive less than they would have without inflation.

Similarly, savers lose when inflation is high, too, as the money they earn from the interest on their savings accounts is worth less than it would have been without inflation. In fact, because savings constitute the loans that make up investment funding, these savers are technically also the lenders (though of course in the real world, these loans are mainly issued by financial institutions like banks), and thus the amount of money available for lending, or investment via the bank, is equal to the amount of savings (a concept known as the savings-investment identity).

In the opposite case, the opposite is true: lenders and savers â€świnâ€ť when low inflation causes the real interest rate to be higher than expected. In this case they earn more than anticipated, while borrowers end up paying more than expected in real terms. Clearly, then, borrowers are the â€ślosersâ€ť in this case.

It may not be immediately clear from these examples, but borrowers â€“ or economic agents taking out loans â€“ are very important to a healthy economy. Thatâ€™s because firms often take out massive loans in order to fund economic projects that can greatly grow the economy, increasing prosperity and economic output (as measured by GDP, for example). So, if rampant inflation pressures savers and lenders to raise interest rates and therefore disincentivizes firms from borrowing funds to make productive investments, the economy can slip and enter a recession. Recall that investment, I, is one of the components of aggregate demand; if I falls because the interest rate is too high, AD can shift to the left, reducing economic output.

Of course, rational economic agents in the real world understand the relationship between the interest rate and inflation. And even though nobody can predict the future, everybody can at least make predictions. So, when borrowers and lenders come together to make a loan agreement in the real world, they wonâ€™t simply ignore the possibility of inflation and suffer the consequences. Instead, their expectations of what future inflation will be changes the terms of their agreement, including the interest rate that theyâ€™ll agree to.

## Adding inflation expectations to the interest rate equation

Our relationship between the two interest rates earlier can be modified to incorporate â€śinflation expectationsâ€ť, which were already hinted at in the discussion above. In macroeconomic models, this term is generally understood to represent the average inflation expected by everyone in the economy.

If a borrower and a lender both expect inflation to remain steady at 1% per year, theyâ€™ll agree to a nominal interest rate that reflects this information. Suppose a borrower and a lender enter a one-year contract. The lender who wants a real return of 5% of the purchasing power of the lent money will suggest a nominal interest rate of 6% instead of 5%. The borrower, who expects to have to pay back an extra 5% of the loanâ€™s worth when the debt comes due, agrees to the 6% rate because he knows heâ€™s really only paying 5% next year once inflation is factored in. Remember, this is because the 1% inflation reduces the purchasing power of money over time.

This behavior allows us to modify the equation for interest rates as follows. Now, i = rd + đťś‹e, where variables are defined nearly the same as above; the nominal interest rate equals the expected real interest rate plus the expected inflation rate at the time the agreement is made. The only changes from above are that r has become rd and đťś‹ has become đťś‹e. Instead of representing the real interest rate and inflation, these variables now represent the desired real interest rate and the expected inflation rate. This accurately portrays the fact that we cannot predict the future.

In summary, economic agents agree to a nominal interest rate that captures the real rate of interest they wish to receive (or pay), according to their expectations of inflation.

## Consequences of inflation differing from expected inflation

This introduces a new dimension of risk to financial agreements. When actual inflation over the period considered equals inflation expectations at the time an agreement was made, nothing changes compared to our analysis before. Rational economic agents are able to account for the inflation. But there are two more cases to now consider: when inflation is greater than or less than expected, what happens?

This slight modification to the interest rate formula has massive implications for economic activity. If the inflation rate is different than expected, suddenly financial contracts become somewhat of a gamble. Itâ€™s simply unknown who will benefit from inflation and who will lose. In times of volatile inflation, more risk-averse individuals might even decide it isnâ€™t worth borrowing or lending at all, since they could end up with a much worse deal than they agreed to.

There are now two sets of equations to consider in parallel. Before considering the role of expectations, we had the formula r = i â€“ đťś‹ for the real interest rate. This equation remains unchanged even though weâ€™ve introduced inflation expectations. Thatâ€™s because once a period of time is over, and a loan (for instance) comes due, the rate of inflation over the period has become known. In other words, this can be thought of as a formula for the actual real interest rate.

But when making an agreement, the inflation rate â€“ and therefore the real interest rate â€“ are unknown, so economic agents must utilize their expectations đťś‹e instead. Above we defined the nominal interest rate theyâ€™ll agree to as i = rd + đťś‹e. Letâ€™s rearrange to get: rd = i â€“ đťś‹e (incidentally, this is known as the Fisher equation in economics). Using the example of a loan, if lenders and borrowers expect a 1% inflation rate (đťś‹e = 1%), and agree to a 5% desired real interest rate (rd = 5%), theyâ€™ll set the nominal interest rate as i = 6%.

Suppose that inflation turns out to be higher than expected such that đťś‹ > đťś‹e, as the actual rate of inflation over the period was đťś‹ = 3%. This means that the real interest rate r turns out to be: r = 6% â€“ 3% = 3%. This is a situation weâ€™ve discussed before. When the real interest rate is lower than expected, borrowers win, because they end up paying back less money in real terms than they agreed to originally. Lenders lose and receive less than they expected.

If the actual rate of inflation had been, say, 0.1%, the situation is reversed. Now, the real interest rate r = 6% â€“ 0.1% = 5.9%. This is more than rd = 5%, which means borrowers must pay back more than they agreed and lenders gain.

## A note on patience and risk

Clearly, then, interest rates are linked to specific periods of time by financial agreements, and often state something about inflation and the state of the economy. But interest rates are affected by other factors, too, like patience and risk.

A more patient individual will have a lower â€śpersonalâ€ť interest rate, because the cost of waiting is not very high for them. In other words, a patient individual is more likely to accept a lower interest rate over long time horizons in an agreement. Conversely, an impatient agent will only agree to higher interest rates for longer-term agreements, ceteris paribus, because waiting is a more painful prospect for them.

And, riskier individuals will be given a higher interest rate than safer borrowers. Thatâ€™s because lenders will demand a higher return when investing their money in a project or an individual that are more likely to default.

## The determination of interest rates

In the real world, interest rates rise and fall based on a wide variety of factors. These include, but are not limited to:

## Government influence on the interest rate

Many of the articles linked in the above list of factors describe their effects on interest rates in detail. But here we consider a few more important points to know about how government and central bank policies interact with interest rates.

First, inflation expectations are clearly very important, and are usually set by precedent. If thereâ€™s been consistent inflation in the economy, people expect interest rates to continue to rise to match it. But of course, inflation doesn't have to behave as expected.

One way the government can improve the situation and bring rising interest rates under control in a case of high inflation is to announce plans that will lower the inflation rate (usually, the inflation rate is the target of concern, not interest rates, but here we ignore this fact for the sake of illustration). If the government is successful in convincing the public that their plans will work, people may believe that inflation wonâ€™t be as bad, and đťś‹e will fall. This means that the nominal interest rate i will fall too. So, any official policy of communication that can help inform the public and convince people that the economic situation is under control can actually help the economy stabilize on its own!

## Limitations of central bank policy

Finally, consider again the equation i = rd + đťś‹e, which shows the nominal interest rate that borrowers and lenders will agree upon. Suppose that there is a period of deflation in the economy, such that economic agents expect that there will be continued deflation in the future; đťś‹e < 0. Also suppose that the desired real rate of interest is smaller in absolute terms than the expected rate of deflation.

What happens in such a scenario when borrowers and lenders try to make a transaction? Since đťś‹e < 0 and đťś‹e is larger in absolute terms than rd, the chosen nominal interest rate i would be negative. But thereâ€™s a catch.

Normally, lenders wonâ€™t agree to a negative nominal interest rate! Thatâ€™s because the nominal interest rate of simply holding onto their own cash is 0% (theoretically; of course in real life there are risks to holding cash). Itâ€™s therefore irrational to make a financial agreement with a negative nominal interest rate; lenders would be better off just holding onto their cash and doing nothing with it.

This scenario â€“ and others like it, where the â€śbestâ€ť nominal interest rate would be below zero â€“ illustrates the â€śzero lower boundâ€ť of interest rates. This is a concern for central banks in times of low inflation and sluggish economic growth, since an interest rate cut is one way to boost the economy. But if the interest rate is already at 0%, it canâ€™t be cut further.

Yet, there are some cases of dire (or just strange) economic circumstances that have had lenders (or savers) agree to financial instruments with negative interest rates, though it is quite rare. In these cases, usually the economy is in such a bad shape that people will accept a negative interest rate in exchange for their savings being secured somewhere.

For instance, in 2014 the European Central Bank (ECB) implemented negative interest rates in order to encourage investment that could lead to inflation and avoid a deflationary spiral. The idea is that since borrowers get paid to borrow money, and savers/lenders receive no or even negative interest for depositing money, investment â€“ and hence aggregate demand and the economy â€“ ought to be stimulated by the negative rates. The ECBâ€™s original rationale for doing so can be read on their website here.

Interest rates are an important part of the puzzle for many other macroeconomic concepts, such as the savings-investment identity, the IS-LM Model, the Fisher Effect, Aggregate Demand, Monetary Policy, Fiscal Policy, Crowding Out, Net Present Value, the Loanable Funds Market, and Banks. For more on how interest rates relate to each topic, see the accompanying Economics Terms A-Z article.

Advanced students interested in exploring how inflation expectations affect prices and interest rates should take a look at John Muthâ€™s Rational Expectations and the Theory of Price Movements, first published in Econometrica in 1961.

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