Interest Rate
The cost of borrowing money expressed as a percentage of the principal amount
What Is an Interest Rate?
The interest rate is the amount paid to borrow money. It is a percentage of the principal, which is the amount loaned. When an individual borrows money, they would have to pay back the original amount borrowed and a percentage of the loan amount, known as interest.
The lender charges the borrower a certain percentage in addition to the money they owe as compensation for the risk of lending money. It can also be thought of as the cost of borrowing money. It is like paying rent on the money you are borrowing.
This rate can be set at fixed or variable rates.
- When it is set at a fixed rate, the interest rate does not change.
- When it has variable rates, this means that it is following a benchmark index.
The rates adjust accordingly to any changes in the index.
The annual percentage rate (APR) is the annualized measure of the interest rate on a loan. Additionally, it is applicable to earnings in a savings account or certificate of deposit (CD) at a bank or credit union.
The annual percentage yield (APY) represents the interest gained from these deposit accounts.
- The interest rate is the amount a lender charges as a percentage of the principal for using assets.
- These rates also apply to earnings from a bank or savings account, with the annual percentage yield (APY) as the interest gained from these accounts.
- Low-risk borrowers tend to have lower rates, while high-risk borrowers have higher rates.
- It is driven by the market environment and is set by the central banks of each country.
Understanding Interest Rate
Interest is the amount of money borrowed to pay for the use of an asset. These assets span from cash to consumer goods to property. This is why it is so important, as it affects the ability to consume and invest in various assets.
It plays an important role in most lending and borrowing transactions. For example, borrowing money to purchase property or mortgages, funding education and tuition, and expanding businesses for long-term growth. The borrowed money can be raised in a lump sum at a certain date or in periodic installments.
Note
The interest rate is known as the cost of debt for the borrower and the rate of return for the lender. The reason the amount to be repaid is more than the borrowed amount is the opportunity cost, which is the cost of using the money for other purposes, such as investing in other assets.
The interest charged is the difference between the original loan and the total repayment at the end of the borrowing period.
When the rate is high, the cost of borrowing becomes more expensive. Similarly, when it is low, the cost of borrowing is cheaper. As such, the rate significantly affects current market conditions and investment strategies.
The interest rate impacts various aspects of our financial life, such as:
- Borrowing money: Borrowers must repay the amount borrowed plus the interest payments, which is the cost of borrowing.
- Lending money: Lenders will set a rate and earn an income on the set rate as an exchange for lending money to others.
- Depositing money: Different interest-bearing accounts will pay the depositors interest income in exchange for agreeing to allow banks to lend depositors’ money to others.
Types of Interest Rates
There are two types of interest rates: simple and compound. The simple version is a more straightforward and basic calculation, while the compound version requires a more complex calculation.
Simple Interest Rate
Simple interest does not account for compounding, so it only applies to the loan's principal.
The formula of the simple interest rate is as follows:
Simple Interest = Principal * Interest * Time
Example: An individual invested $100,000 at a 5% annual rate over a period of one year. Then, the interest earned after one year is:
$100,000 x 5% x 1 year = $5,000
If the period is over one year, let’s say 30 years, then the interest earned would be:
$100,000 x 5% x 30 years = $150,000
Compound Interest Rate
The compound interest rate accounts for compounding and can be thought of as interest gaining interest over time. It has a more complex calculation, and the interest earned depends on the frequency of compounding, whether daily, monthly, or yearly.
The formula of the compound interest rate is:
compound interest = p * [(1+ interest rate)n - 1]
Where:
- p = Principal
- n = Number of compounding periods
Using the example from above, the interest earned is
$100,000[(1 + 5%)30 -1] = ~$332,194
This is much higher than the interest earned calculated in the simple interest formula ($150,000).
Simple Vs. Compound Interest Rate
The table below shows the difference between simple and compound interest rates in terms of complexity, effect of time, and interest owed.
Simple | Compound | |
---|---|---|
Complexity | Simple, no compounding | Complex, has compounding |
Effect of time | No effect | Grows with time |
Interest owed | Lower | Higher |
The disparity between simple and compound becomes greater as the lending period becomes longer. In our example, the compound version accumulates over time, surpassing the simple version by almost $200,000 at the end of 30 years.
Investments with Interest Rates
When the rate of interest is stated as compound interest, it means that the interest for any given period will also earn interest in future periods. This process is known as compounding.
If the rate of interest is compounding, traders would be interested in knowing in advance the stability of their money owed at a potential future date.
The price of an investment at a future time is referred to as the destiny fee of the funding made on the cutting-edge time.
Future value can be calculated as follows:
If A is the amount of investment, r is the rate of interest, and FV is the future value at the end of the n years, then
FVn = A x (1 + r)n
For example, Mohan deposited $50,000 on January 1, 2009, in an investment that promised 12% compound interest. What will be its future value on December 31, 2010?
Future value on December 31, 2010 = $50,000 x (1 + 0.12)2 = $62,720
Present value refers to the amount that is to be deposited today in order to receive a known amount at a known future time. Present value is very important in the valuation of financial securities, including derivative securities.
Note
The value of any financial security is calculated as the present value of all the future cash flows provided by the security. The calculation of present value is known as discounting.
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The present value of a future amount at the end of n years is calculated as
Present value = FV /(1 + r)n
The expression (1 + r)n is known as the present value index factor.
For example, Oliver wants to accumulate $125,000 in three years to buy a car. So, the amount invested by him if the interest rate is compounded annually at 9% will be:
Present value = 125,000 /(1+0.09)3 = $96,522.94
Present Value For Different Compounding Periods
The amount of the payment or investment, the interest rate, and the period of compounding are only a few of the variables that affect the present value of a future payment or investment.
How frequently interest is calculated and applied to the investment is referred to as the compounding period.
Depending on the chosen compounding period, a future sum of money has a different present value. In general, the current value increases with the frequency of compounding. This is because interest is earned at a higher rate when compounding occurs more frequently.
The method for estimating the future value for various compounding periods can also be used to compute the present value for those periods.
The present value of a sum to be received after n years is calculated as
PVn = FV /(1+r/m)mn
Where,
- m is the number of compounding periods.
If it is continuous compounding, the present value is calculated as
PV = FV x e-rt
Where,
- t is the number of years, and
- e is exponential.
For example, calculate the present value of $200,000 to be received in 3 years if the interest is compounded semiannually at the rate of 10%.
PV = 200,000/(1+ 0.1/2)2x3 = $149,243.08
If continuous compounding,
PV = 200,000 x e-(0.1)x(3) = $148,163.64
Future Value For Different Compounding Periods
The process of adding interest from an investment back into the principal sum is known as compounding interest, which enables the investment to grow even faster over time.
The future value of a sum to be received after n years is calculated as
FVn = PV x (1+r/m)mn
Where,
- m is the number of compounding periods.
If it is continuous compounding, the future value is calculated as
FV = PV x ert
Where,
- t is the number of years
- e is exponential.
The frequency of this compounding can significantly affect the investment's potential return.
However, if the interest is compounded quarterly, then after one year, your investment would be worth $10,509.45 ($10,000 x (1 + 0.05/4)^4), which is slightly more due to the compounding effect happening four times a year instead of just once.
As we move towards shorter compounding periods, the future value of the investment will continue to increase.
If the interest is compounded monthly, then after one year, your investment would be worth $10,511.62 ($10,000 x (1 + 0.05/12)^12), which is even more than the quarterly compounding scenario.
If the interest is compounded continuously, then the future value will be,
FV = 10,000 x e0.05 = $10,512.71
Risks Associated With Interest Rate
While the investor is aware of the amount he'll get at the realization of the investment duration, the funding is stated to be risk-free.
Understanding the risks associated with fixed-income security is important before understanding what a risk-free interest rate is. Here, we take into account the dangers of bond investing.
When an investor buys a bond, they will eventually get the bond's face value as well as periodic payments.
The market price in effect at the time would be paid to the investor if they choose to sell the bond before it matures.
However, there are some uncertainties concerning the number of fees to be obtained through the bondholder.
1. Interest rate risk
The coupon payment that one would get is uncertain if the bond has a variable coupon rate.
Future interest rate ambiguity also has an impact on the bond's value. Bond values will vary, falling as interest prices rise and growing as they upward push, relying on the bond's interest fee.
As a result, an investor who wants to sell the bond earlier than it matures may even deal with the uncertainty of no longer knowing the bond's sale price.
2. Default risk
This measures the uncertainty of whether the borrower will be able to make periodic coupon payments as well as the uncertainty of the principal amount at maturity.
Within the case of government bonds, there can be no threat that the government will fail to make its normal payments. However, there's a chance that the business enterprise will not fulfill its duties when it buys organization bonds.
3. Call risk
This is a reference to the ambiguity over (i) whether the callable bond's issuer will call the bond before maturity and (ii) the moment at which they would make the call if they decide to do so.
4. Liquidity risk
Selling a bond at its fair value will be simple if there is enough demand for bonds.
But, it will be exceedingly challenging to locate a buyer if there is very little demand for a bond. If one needs to sell in such a scenario, one must accept the rate being paid for the bond, which is usually less than its fair cost.
Bonds that are frequently exchanged are said to be illiquid, whilst those that are heavily traded are thought to be extremely liquid.
Risk-Free Interest Rates
Given that bond investment involves these risks, a risk-free investment is one that has no liquidity risk, default risk, call risk, and interest rate risk.
Usually, the following are considered risk-free.
Government Security Rates
The central government issues government securities in an over-the-counter market that is very active with participation by banks and other financial institutions.
It has no liquidity risk or default risk, but there may be interest rate risk on long-term government securities.
It's widely assumed that short-term period authorities securities are danger-free, and the yield is considered risk-free interest prices. It is used in the valuation of options, futures, and forward rates.
Note
Non-callable bonds have no call risk.
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Interbank Rates
Interbank rates are the rates at which one bank can borrow or lend to other banks. These rates are determined every day on the basis of demand for interbank borrowing and lending.
It has been used as a reference for floating rate loans, interest rate swaps, forward rate agreements, and currency swaps.
The most important international interbank is the London Interbank Offer Rate (LIBOR).
Repurchase Agreement Rates (Repo Rate)
A repurchase settlement is a settlement among parties where one party agrees to sell government securities at a specific time and buy them again at a later time at a special rate.
Buying price after selling is higher than the selling price. In practice, there is no exchange of securities at the time of either selling or buying.
The repurchase agreement can be for any period, depending on the needs of the party that wants to enter into the agreement.
Note
The most common period for repurchase is an overnight repurchase agreement, where the loan is secured only for overnight use.
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Since government securities are used as collateral, there will be no default risk, call risk, liquidity risk, or interest rate risk.
How are interest rates determined?
One of the key drivers of how it is determined is the market environment of an economy. Generally, it is set by a country’s central bank, which will affect how the banks within the country determine the annual percentage range (APR) they will offer.
The cost of debt increases if the country's central bank sets a high interest rate. This also affects the market landscape, as people will be deterred from borrowing, which slows market activity. Additionally, the rate set by the central bank tends to follow the inflation trend.
In an economy with high inflation, the central banks will usually tighten their monetary policy by pushing the rate up.
However, this will cause more people to want to save instead of spending money. This is because they can save more from the savings rate than actually consuming products.
Similarly, investors may halt activities in the stock market, as it would be more beneficial to take advantage of the higher savings rate than the potentially lower returns from the stock market.
Since the cost of debt is higher, there would be less capital to fund various businesses. A high rate could lead to lower business valuations and a shrinking economy.
On the other hand, when the economy needs some stimulation or growth, there will likely be a lower rate set. This means that loans become cheaper, so there is a higher borrowing rate.
Due to the low savings rate, businesses and individuals are more inclined to spend and purchase riskier assets instead of saving their money. As spending increases, more money is injected into the economy, which could lead to market expansion.
Overall, although borrowers generally prefer a lower rate under normal economic conditions, it is constantly monitored due to potential disequilibrium. Inflation may occur when an economy starts to become overheated, so interest rates must be raised again.
Interest Rate FAQs
APR is the set annual interest rate for one’s loads, such as credit card loans, and any associated costs or fees. It is the total cost of the loan, which is presented as a percentage. An APR makes it easier for borrowers to compare different lenders and loan options.
The interest rate on credit cards is an APR. When credit card companies issue cards, they must release the APR associated with the card. The APR does not take into account compounded interest.
A bond is a debt instrument that pays a fixed rate over time.
So, when the interest rate increases, the previously purchased bond earns less profit at its fixed rate, making it less valuable. As a result, fewer investors would want to buy that bond, which decreases the bond price.
On the other hand, when it decreases, the bond earns more profit at its fixed rate, making it more valuable. So, there is a higher demand for this bond, which increases its price.
Using raised interest rates to control inflation has been the reality of our market environment since the recovery from the pandemic.
In short, increasing the interest rate increases the cost of borrowing, which then slows down consumer spending, business growth, and investing in the stock market, which have all been drivers of inflation. Ultimately, these factors contribute to an economic contraction that lowers inflation.
Here is a video from the Economist that explains more of our current situation:
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