An interest rate is a percentage of interest paid on a borrowed or invested sum. The interest rate is typically expressed as an annual percentage of the principal. It determines the cost of borrowing money or the return on investment. Central banks use interest rates as a tool to manage monetary policy and stabilize the economy.
1- Components of Interest Rate
A loan is a transaction that is considered when one party is willing to postpone the consumption of some of their resources. At the same time, another party wishes to bring forward the consumption of resources that they will earn in the future. The party postponing their consumption becomes a lender, while the party bringing forward their consumption becomes a borrower.
As people are often impatient, lenders often ask to be rewarded for postponing their consumption. At the same time, borrowers are often willing to give up more of their future resources than they can now receive. This idea is called Irving Fisher’s impatience theory of interest.
But there is more to interest rate than impatience alone. In other words, lenders have reasons for charging an interest more important than their impatience. Loans are very rarely made in terms of a good or service. Instead, loans are often made in terms of money. In the 21st century, we use fiat money, which is valuable only by convention because we can use it to acquire goods and services.
Because of inflation, the purchasing power of money declines as time passes. So an important role of interest is compensating the lender for the reduction in the purchasing power of their money. The consumer price index (CPI) is the official way to measure inflation. You can use WOWA’s inflation calculator to see how fast the Canadian dollar has lost its value in recent history.
But even if lenders were very patient and there was no inflation, there is still an essential role for interest. When lending, you always accept the risk that a borrower might be unable or unwilling to pay his debts. The interest should compensate lenders for the risk of a possible default on a loan.
Lastly, extending a loan requires motivation (profit margin) in addition to documentation, record keeping, transactions and more. Depending on the type of loan, the lender might charge an administration fee separately, or they might include administrative costs in the interest.
We can summarize this discussion on interest rates by breaking the rate of interest down into three (potentially four) components.
Components of Interest Rate
Interest Rate = Time Value of Money + Expected Inflation Rate + Risk Premium (+ Administrative Costs).
Consider a case where you are asked for a $100 loan. Suppose you know that with a 90% likelihood, the borrower will pay your money back, while with a 10% likelihood, the borrower will disappear, and you won’t receive anything. To avoid losing money on this loan, you would ask for x dollars back such that 0.9x=$100. In other words, you would need to charge a risk premium of 11.11% for your expected return to stay the same as what you originally lent.
In many cases, like credit card interest or payday loan interest, the risk premium is the most significant component of the interest rate. Yet, in real-world situations, it is often challenging to determine the probability of loss on loan to a specific borrower and, thus, the required risk premium on that loan. In a financial context, default refers to a failure to pay back a loan according to the terms agreed upon in the loan contract.
A default can happen for various reasons, such as a lack of income or other financial difficulties. When a borrower defaults on a loan, the lender might be able to work with the borrower on restructuring the loan and allowing the borrower to pay their debt on a modified schedule. Such a restructuring might enable the lender to avoid any loss on the loan.
Suppose the borrower and the lender are unable or unwilling to restructure the loan. In that case, the lender may take legal action to recover the debt by seizing the borrower's assets or garnishing their wages.
In some cases, the loan may be sold to a collection agency or a debt buyer who will try to recover the debt on behalf of the lender. Defaulting on a loan can have severe consequences for the borrower's credit score and may make it difficult to obtain credit in the future.
The likelihood of default on a loan would depend on many factors, including macroeconomic factors such as the state of the job market (unemployment rate), average incomes, inflation rate, foreign exchange rates and central bank policy. It also depends on factors specific to each borrower, like the borrower's net worth, employment type, annual salary (or other income) and spending habits.
There is no general formula for predicting the likelihood of default; even if we can predict the possibility of bankruptcy, there is no general formula to predict the amount of loss resulting from any default. Yet lending is the lifeblood of a modern economy, and if the lending process stops, a dramatic reduction in production and consumption will ensue. The result would be a dramatic decrease in living standards.
Thus there are many lenders in each economy, and each has developed its own models for predicting their potential loss on each loan, thus deciding the risk premium for each loan. As a result, there is no single rate of interest. Instead, there are many rates of interest in each economy.
Loans can be secured or unsecured. A secured loan has collateral. Collateral refers to assets pledged as security for a loan or other debt. If the borrower cannot repay the loan, the lender may seize the collateral to recoup their losses.
Common examples of collateral include real estate, vehicles, jewelry, stocks and bonds.
Collateral can also refer to a guarantee or security provided to secure a loan or credit. Collateral can dramatically reduce the risk of loss on a loan because in a secured loan if the borrower defaults, the lender can cash out the collateral and use the proceeds to repay the loan. In comparison, an unsecured loan is a much riskier endeavour for the lender.
1-2 Expected Inflation + Time Value of Money
Expected inflation and the time value of money are conceptually distinct, yet we cannot observe them independently. In finance, we often assume that there is no risk in lending money to the government that has issued the loan's currency. The interest rate paid by the government is considered to be the risk-free rate.
In other words, you can determine the risk premium on any loan by subtracting the interest rate the government is paying from the interest rate of that loan. But there is no easy way to separate the expected inflation rate from the time value of money, and we can only measure them together.
Interest Rate Formula
A helpful formula for the interest rate:
Rate of Interest = Risk-Free Rate of Interest + Risk Premium
1-2-1 Yield Curve
The Risk-free rate of interest includes both the expected inflation rate and the money's time value. The expected inflation rate and time value of money both depend on the time interval under consideration. ƒ
For example, your expected inflation for 2023 might be significantly different from your expected inflation for 2024. Thus the risk-free rate is discovered in the market for each term independently when government debt securities are traded for various lengths of time.
For example, in Canada, we infer the 5-year risk-free rate from the yield of Canada's 5-year bonds and the 10-year risk-free rate from the yield of the Government of Canada's 10-year bonds. Below is Canada’s yield curve for January 2023 and November 2021.
We usually expect a higher yield the lengthier the term of the loan gets because further out in the future is more uncertain. So the expectation for the yield curve is to be positively sloped, as is the case with Canada’s yield curve in November 2021. This contrasts with the January 2023 yield curve, which is negatively sloped. A negatively sloped yield curve means that investors expect short term yields to decline. Since a decline in short term yields often follows a decline in economic activity, an inverted yield curve is often considered a harbinger of recession.
Canada Yield Curve
1-3 Administrative Fee
A lender might directly charge an administrative fee, or it might consider its administrative cost and expected profits when quoting its rate. Thus when comparing different lending products, it's best to compare their Annual Percentage Rate (APR), which includes any potential fee. You can use WOWA’s APR calculator to compare different lending products.
2- Measures and Effects of Interest Rates
2-1 Yield on Bond Assets
An asset has monetary value and can be owned by an individual or organization. Assets include cash and cash equivalents, investments, real estate, and personal property such as vehicles or equipment. They can also have intangible assets such as patents, trademarks, and copyrights.
To make it short and precise, we can define an asset as something which produces goods or services. A service is an activity or series of activities that benefit the customer without transferring ownership of a physical item. For example, an apple tree produces apples, so it is an asset, and your house provides you with shelter. The shelter is typically considered to be a service. Thus your house is an asset.
In finance, there are two important asset classes, stocks and bonds. A bond is a debt security issued by a corporation, municipality, or government entity, known as the issuer. When an investor buys a bond, they essentially lend money to the issuer, who promises to pay back the principal (or face value) of the bond when it matures and make regular interest payments (coupons) to the bondholder. The maturity date is when the issuer will pay back the bond's principal amount to the bondholder, and the coupon rate is the percentage of the bond's face value paid to the bondholder as interest.
Bonds are considered fixed-income investments and are generally less risky than stocks but riskier than cash or cash equivalents. They are often used by investors to diversify their portfolios and by companies and governments to raise capital for various projects.
2-2 Is Interest Rate a Price?
It is tempting to think of interest rate as a price for using money, as rent is a price for using a property. By considering interest as the price for the use of money, which here stands for capital, we are led to consider the supply and demand for loans. We are led to think about how much savings are accumulated in the economy and how much demand for loans exists in the economy.
But this analogy is very limited. Rental houses in any locality are approximately conserved over short periods. It takes considerable time and capital to build new homes, but when they are built, they will provide shelter for decades. As a result, short-term fluctuations in the number of dwellings in each city are limited.
In comparison, fiat money is constantly created and destroyed in our fractional reserve banking system. Each time the Bank of Canada makes a purchase, money is created, while each time the Bank of Canada sells or redeems any of its investments, money is destroyed.
It is important to note that the creation and annihilation (destruction) of money is not limited to the Central Bank. Each time a commercial bank extends a loan, money is created, and money is destroyed when a borrower pays his debt back to a commercial bank.
People's decision to defer their spending and save more puts downward pressure on interest rates, and their decision to bring forward spending and borrow more puts upward pressure on interest rates. But there is a much more potent force which affects interest rates.
2-3 Effect of Interest Rates
Before considering the most potent agent affecting interest rates, we should consider the effect of interest rates on our economy. We mentioned that bonds are debt instruments which trade in the market. Their price determines their yield, and if a central government issues them in its domestic currency, they are considered risk-free. The yield on these bonds is the risk-free rate of interest.
The assumption that lending to the government is risk-free is reasonable for many countries like Canada, England, Belgium and Denmark, which have never defaulted on their national debt in recent history. Before talking about who affects interest rates the most, we should mention the effects of interest rates on the economy.
An interest rate is an exchange rate between futures money and today’s money. As a result, higher interest rates would encourage people to postpone their consumption and investment plans. In comparison, lower interest rates would encourage economic actors to bring forward their consumption and investment plans.
An increase in spending would increase gross domestic product and employment, while a decrease in spending would decrease both gross domestic product and employment.
So initially, a low interest rate seems to be very desirable. The problem is that increased demand for goods and services produced by low interest rates can outpace the economy’s capacity for producing goods and services. This is a situation where too much money is chasing too few goods and services. This situation would result in inflation.
Inflation is harmful because it increases uncertainty regarding future inflation, complicating investment and savings decision-making. Inflation also increases the opportunity cost of keeping money, often resulting in a wealth transfer from those depending on a fixed income to asset holders. In extreme cases, inflation would cause hoarding, which in turn results in a shortage of goods and waste.
2-4 Bank of Canada’s Role in Interest Rates
Given how important money, credit and interest are to the functioning of a modern economy, it is very important to separate monetary policy from politics. In modern economies like Canada, the central bank is able to make monetary policy decisions independent of political interference.
Bank Of Canada
Bank of Canada (BoC) is a crown corporation created in 1934 by the Bank of Canada Act, around two decades after the creation of the Federal Reserve System in the US. BoC is responsible for conducting monetary policy and promotion of a safe and sound financial system in Canada. BoC is also mandated to protect the value of the national currency and to mitigate fluctuations in production, trade, prices and employment.
BoC shares are held by the Minister of Finance on behalf of the King. Members of the board of directors of the BoC are appointed by the government. BoC has signed a contract with the Department of Finance to conduct monetary policy with the aim of achieving a 2% inflation target. With a target of 2%, the bank is concentrated on bringing inflation to a range of 1% to 3%.
Bank of Canada Overnight Rate History
Bank of Canada rate over the past 6 decades. This is the interest rate BoC charges to commercial banks when they borrow money from BoC. This rate is currently 25 basis points higher than the BoC target overnight rate. The BoC target overnight rate is the rate that the BoC wants commercial banks to charge each other for overnight lending.
Bank of Canada’s main tool for implementing monetary policy and achieving its inflation target is BoC target overnight rate. Bank of Canada is currently using a floor system in which the target rate is the same rate that BoC pays to commercial banks' deposits. While the market price of government bonds determines the funding cost for term loans, the BoC overnight target determines the funding cost for day-to-day interest rates. As a result, the short end of the yield curve is set by the BoC. BoC also has the ability to affect medium and long-term rates by trading financial instruments (mostly bonds). BoC extraordinary power in affecting the bond market is because of its unlimited liquidity.
2-5 Prime Interest Rates
Each lending institution sets a prime lending interest rate, serving as an index for its lending products. For example, we have RBC prime rate, TD prime rate, Scotia prime rate, etc. The interest rate on many credit products offered by Canadian banks is in the form of Prime Rate + Margin. This margin can be positive or negative and depends on the credit risk in the loan.
For example, variable mortgage rates, line of credit rates, HELOC rates, most car loan rates and student loan rates use this formula and are based on the prime rate. Practically all Canadian financial institutions are using the same prime rate. The BoC choreographs the movements of the prime rate. Each time BoC announces a change in its overnight target rate, Canadian banks followed by announcing a change in their prime rate. In the 21st century, with few exceptions, the magnitude of changes in the prime rate matches changes in the overnight target rate.
3- Interest Rates for Different Financial Products
Interest Rate Range for Representative financial products during second half of January 2023
Best Advertised Rate
15th Best Advertised Rate
Insured 5 Year Fixed Mortgage
Uninsured 5 Year Fixed Mortgage
Insured 5 Year Variable Mortgage
5 Year GIC
1 Year GIC
Uninsured 5 Year Variable Mortgage
3-1 Credit Card Interest Rates
Credit cards are unsecured and very convenient to use. At the same time, most credit cards in Canada have high interest rates, typically around 20% per year. This high interest rate prevents financially informed and well-off consumers from using their credit cards for borrowing. They use credit cards for spending but pay their monthly bill to avoid interest. Thus credit card borrowers are more likely to default on their debt compared with the average consumer. Yet there are some credit cards with relatively low interest rates.
At large financial institutions, this margin is often small or even negative. This is because larger Canadian banks often have a higher administrative cost of issuing the GIC and access to low-cost sources of money like chequing accounts. Smaller financial institutions often do not have as much access to low-cost money and are thus willing to offer a higher margin to attract more GIC investors.
Car loan rates have a wide distribution. Technically a car loan is a secured loan, but it is more difficult to possess a car than to possess financial assets or to possess real estate. Thus from a lender's perspective, they are the least secure of secured loans. Yet you might see very low rates for some new cars when a car company engages in providing financing to facilitate the sale of its products.
3-4 Mortgage Interest Rates
A secured loan with real estate as its collateral is called a mortgage. In terms of volume, mortgages are the largest lending product offered by Canadian financial institutions. When taking out a mortgage, a borrower has to make an important decision. Do they want to pay interest based on the short end of the yield curve or based on some point in the middle of the yield curve?
Variable-rate mortgages and adjustable-rate mortgages both offer rates at the short end of the yield curve, while fixed-rate mortgages offer rates based on a point in the middle of the yield curve. If you choose either a variable interest rate or an adjustable interest rate mortgage, you will be charged an interest = Prime Rate + Delta where the delta will stay the same during your mortgage term while the Prime Rate might change by your financial institution any day based on changes to the short end of the yield curve. While in a fixed-rate mortgage, the interest rate will stay the same during your mortgage term.
3-5 Saving Account Interest Rate
Savings Accounts are a great option for keeping your emergency savings. Savings accounts in Canadian financial institutions are safe as they are insured by crown corporations like CDIC or its provincial counterparts. The most important factor determining the interest rate on savings accounts is a financial institution’s desire and need to attract your deposit. Some institutions have branded a savings account as High Interest Savings Account in order to attract more rate-sensitive customers.
3-6 Line of Credit Rate
Lines of credit in Canada almost always have a variable interest rate. In other words, their interest rate is prime rate + delta, where delta is fixed in the line of credit contract, but the prime rate can be changed by the financial institution at any time. Prime rates often change based on changes in the Bank of Canada policy rate.