1. Introduction
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized. The interest rate has been characterized as “an index of the preference for a dollar of present [income] over a dollar of future income” [1] . The borrower wants, or needs, to have money sooner rather than later, and is willing to pay a fee-the interest rate-for that privilege.
2. What Is Interest Rate?
Interest rate is the amount charged over and above the principal amount by the lender from the borrower In terms of the receiver, a person who deposits money to any bank or financial institution also carns additional income considering the time value of money, termed as interest received by the depositor. Interest rates on borrowings and deposits may defer considering the purpose and to whom the amount is given Interest Rate on Borrowings Borrowing has become prevalent in terms of the smooth functioning of trade practices and proper regulation of money in the economy, and the process of borrowing money has also been relaxed to help businesses grow Borrowings not only ease money problems but also helps the borrower in planning the finances better Interest rates on borrowings are fixed depending on the type of borrower and the credit rating associated with him. Suppose the borrower has a low credit rating. In that case, it might be possible that banks might not lend money at all or by charging extreme interest rates or keeping the double amount of collateral security. Private lenders also provide loans to borrowers, but their terms and conditions might differ from the conventional loans obtained from banks or financial institutions [2] . They might charge hefty interest on the sun lent with certain other additional conditions. In the event of default, banks or financial institutions stop charging interest and reclassify the assets in their books. In the event of pre-payment, a penalty and interest are charged from the borrower to avoid the loss of regular income considering the time value of money.
* An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you’re a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
* An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you’re a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.
* Interest Rates a charge on profits is not always welcomed, but all appreciate income in any form. Interest is income earned on the funds utilized by the person holding the same.
* The charging of interest for lending money has not always been and is specifically condemned in both the Bible I usury acceptable practice and in Shariea law, and modern Islamic banks operate only on the basis of profit.
In modern financial markets, however, the distinctions between interest, rent, profit and captral appreciation are not clear-cut. The Lument utly debated proposal on the taxation of interest within the Eu has illustrated the difficulty of reaching legally precise definitions in economic theory, interest is the price paid for inducing those with money to save it rather than spend it, and to invest in long-term assets rather than hold cash. Rates reflect the interaction between the supply of savings and the demand for capital; or between the demand for and the supply of money (icouponi a) Rates of interest can be expressed as a percentage payable value of a sum payable idiscountedi usually per annum; or as the present There is an inverse (imaturityi the date of) at some future date relationship between the prevailing rate of interest at any one time, and Le, bond prices the discounted value at that time of assets paying interest fall when yields increase Ireali and inominali An important distinction must be made between rate, nicouponi le n interest rates.
A real rate of interest is the nominal less the rate at which money is losing its value Calculating real rates, however, presents methodological problems, since there are significantly different ways of calculating rates of inflation Inflationary expectations, however, are one of the most important determinants of interest rates. Broadly, savers demand a real return from their investments.
Changes in the forecasts of future inflation are therefore reflected in the current prices of assets. The effect on bonds of varying attract savings at a very much lower rates of interest than corporate Countries with high levels of existing debt may junk bonds issuers of have to pay higher rates on government harrowing than comtries where will isovereign debt the risk of default is less. Indeed, the guarantee that be repaid on maturity has frequently allowed governments to borrow at. Negative real rates of interest within any economy there will therefore be a multiplicity of interest rates. I yield curvei maturity, for example, can be charted as shifts in the Rates of interest also reflect varying degrees of risk. A body with a rock-solid credit-rating, like the European Investment Bank, will be able to reflecting varying expectations and risks. The markets for different assets will influence each other as savers shift their physical and financial portfolios between cash, interest-bearing securities, equity in firms, complex derivatives, real estate, antiques, etc. Financial institutions and large corporations will behave differently from small savers and small businesses.
3. Interest Rate Definition
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (apr).
An interest rate can also apply to the amount earned at a bank or credit union from a savings account or certificate of deposit (cd). Annual percentage yield (apy) refers to the interest earned on these deposit accounts.
4. Understanding Interest Rates
Interest is essentially a charge to the borrower for the use of an asset. Assets borrowed can include cash, consumer goods, vehicles, and property. Because of this, an interest rate can be thought of as the “cost of money”—higher interest rates make borrowing the same amount of money more expensive. Interest rates thus apply to most lending or borrowing transactions. Individuals borrow money to purchase homes, fund projects, launch or fund businesses, or pay for college tuition. Businesses take out loans to fund capital projects and expand their operations by purchasing fixed and long-term assets such as land, buildings, and machinery. Borrowed money is repaid either in a lump sum by a pre-determined date or in periodic installments. For loans, the interest rate is applied to the principal, which is the amount of the loan. The interest rate is the cost of debt for the borrower and the rate of return for the lender [3] . The money to be repaid is usually more than the borrowed amount since lenders require compensation for the loss of use of the money during the loan period. The lender could have invested the funds during that period instead of providing a loan, which would have generated income from the asset. The difference between the total repayment sum and the original loan is the interest charged. When the borrower is considered to be low risk by the lender, the borrower will usually be charged a lower interest rate. If the borrower is considered high risk, the interest rate that they are charged will be higher, which results in a higher cost loan.
5. Types of Interest Rate
1) Simple
2) Compound
5.1. Simple Interest Rate
Simple Interest: Formula
If interest is calculated uniformly on the original principal throughout the loan period, it is called simple interest. The simple interest formula is given by
(1)
when P = Principal, R = Rate of interest per annum and T = time.
The money borrowed initially is called the principal amount of the sum. It is known as the original sum also. The amount is the total money that includes the principal and the interest paid by the borrower to the lender. The interest of 
100 for 1 year is known as the rate per annum. Time is the period for which the sum is given to the borrower. It can be expressed in years, months, and days as well.
An example:
If you take out a $300,000 loan from the bank and the loan agreement stipulates that the interest rate on the loan is 4% simple interest, this means that you will have to pay the bank the original loan amount of $300,000 + (4% × $300,000) = $300,000 + $12,000 = $312,000.
The individual that took out a loan will have to pay $12,000 in interest at the end of the year, assuming it was only a one-year lending agreement. If the term of the loan was a 30-year mortgage, the interest payment will be:
Simple interest = $300,000 × 4% × 30 = $360,000
A simple interest rate of 4% annually translates into an annual interest payment of $12,000. After 30 years, the borrower would have made $12,000 × 30 years = $360,000 in interest payments, which explains how banks make their money.
5.2. Compound Interest Rate
Some lenders prefer the compound interest method, which means that the borrower pays even more in interest. Compound interest, also called interest on interest, is applied both to the principal and also to the accumulated interest made during previous periods. The bank assumes that at the end of the first year the borrower owes the principal plus interest for that year. The bank also assumes that at the end of the second year, the borrower owes the principal plus the interest for the first year plus the interest on interest for the first year.
The interest owed when compounding is higher than the interest owed using the simple interest method. The interest is charged monthly on the principal including accrued interest from the previous months [4] . For shorter time frames, the calculation of interest will be similar for both methods. As the lending time increases, however, the disparity between the two types of interest calculations grows. Using the example above, at the end of 30 years, the total owed in interest is almost $700,000 on a $300,000 loan with a 4% interest rate.
The following formula can be used to calculate compound interest:
(2)
where:
p =principal;
n = number of compounding periods.
5.3. Compound Interest and Savings Accounts
When you save money using a savings account, compound interest is favorable. The interest earned on these accounts is compounded and is compensation to the account holder for allowing the bank to use the deposited funds.
If, for example, you deposit $500,000 into a high-yield savings account, the bank can take $300,000 of these funds to use as a mortgage loan. To compensate you, the bank pays 1% interest into the account annually. So, while the bank is taking 4% from the borrower, it is giving 1% to the account holder, netting it 3% in interest. In effect, savers lend the bank money which, in turn, provides funds to borrowers in return for interest.
Also, may be divided as in Figure 1 below.
6. Other Types of Interest Rate
6.1. Central Bank Base Rate
● The base rate is the interest rate which the central bank lends money to the commercial banks.
● This base rate is the most important interest rate because it tends to influence all the other interest rates in the economy.
● If the central bank increases the base rate. Commercial banks find it more expensive to borrow from the central bank. Therefore, they pass this onto their consumers.
● Indirectly, the central bank rate affects all interest rates in the economy— from mortgage rates to the saving rate you get in a savings account [5] .
6.2. Commercial Bank Rate
Commercial banks are free to set their own interest rates, but it tends to be strongly influenced by the central bank base rate. If they find it more expensive to borrow from the central bank, they tend to increase their commercial rates.
Standard variable rate (svr). This is the most common lending rate for the bank. Sometimes, banks may give discounts to consumers from their svr, but the svr will be the main lending rate for a bank.
![]()
Figure 1. Comparison between Cost of the borrowing and Return on saving.
6.3. Mortgage Interest Rates
Mortgages are a type of loan secured against the value of a house. Banks are willing to lend large sums at relatively low interest because if the mortgage holder defaults, the bank can legally reclaim the house and secure the value of its loan.
● Fixed mortgage rates. Banks may offer a fixed mortgage rate (e.g., 2 years, 5 years, 10 years) this gives mortgage holders greater security over the cost of monthly mortgage payments.
● Tracker mortgage rates. Banks may offer a mortgage where the mortgage rate follows the central bank base rate. If the central bank reduces base rates to 0.5%, the mortgage rate will fall to a similar level.
● Variable mortgage rate. A mortgage rate which is determined by the banks svr.
7. Saving Rates
● Interest rate on current account (perhaps 0.5%). Many banks may pay savers very little interest for their savings in a current account. This is because savers can have instant access to their savings so the bank needs to keep more cash in reserve and these cash deposits are not very profitable for the bank.
● Interest rate on savings account (perhaps 2% - 4%) For saving accounts, banks can pay a higher rate of interest. This is because money is less likely to be withdrawn. The bank may even place limits on access to funds (e.g., you have to give 7-day notice) this means the money can be more profitable for banks as they use it to lend to other people.
8. Loanable Funds Theory
The loanable funds theory states that interest rates will be determined by the supply and demand for funds. If people save more, there will be more funds for investment, this will reduce interest rates [6] . If demand for borrowing increases, this will push up the cost of borrowing (Figure 2).
9. Borrower’s Cost of Debt
While interest rates represent interest income to the lender, they constitute a cost of debt to the borrower. Companies weigh the cost of borrowing against the cost of equity, such as dividend payments, to determine which source of funding will be the least expensive. Since most companies fund their capital by either taking on debt and/or issuing equity, the cost of the capital is evaluated to achieve an optimal capital structure.
10. Annual Percentage Rate (apr) vs. Annual Percentage Yield (apy)
Interest rates on consumer loans are typically quoted as the annual percentage
![]()
Figure 2. The equilibrium interest rate is at R1 when demand equals supply for loanable funds. In the credit crunch (2008-11), a shortage of funds pushed up bank rates.
rate (apr). This is the rate of return that lenders demand for the ability to borrow their money. For example, the interest rate on credit cards is quoted as an apr. In our example above, 4% is the apr for the mortgage or borrower. The apr does not consider compounded interest for the year. The annual percentage yield (apy) is the interest rate that is earned at a bank or credit union from a savings account or cd. This interest rate takes compounding into account.
11. Rates Determination
The interest rate charged by banks is determined by a number of factors, such as the state of the economy. A country’s central bank (e.g., the federal reserve in the u.s.) sets the interest rate, which each bank uses to determine the apr range they offer. When the central bank sets interest rates at a high level, the cost of debt rises [7] . When the cost of debt is high, it discourages people from borrowing and slows consumer demand. Also, interest rates tend to rise with inflation.
To combat inflation, banks may set higher reserve requirements, tight money supply ensues, or there is greater demand for credit. In a high-interest rate economy, people resort to saving their money since they receive more from the savings rate. The stock market suffers since investors would rather take advantage of the higher rate from savings than invest in the stock market with lower returns. Businesses also have limited access to capital funding through debt, which leads to economic contraction.
Economies are often stimulated during periods of low-interest rates because borrowers have access to loans at inexpensive rates. Since interest rates on savings are low, businesses and individuals are more likely to spend and purchase riskier investment vehicles such as stocks. This spending fuels the economy and provides an injection to capital markets leading to economic expansion [8] . While governments prefer lower interest rates, they eventually lead to market disequilibrium where demand exceeds supply causing inflation. When inflation occurs, interest rates increase, which may relate to walras’ law.
12. Factors That Indicate or Determine Magnitude of Interest in Economy
* The strength of the economy and the willingness to save. Interest rates are determined in a free market where supply and demand interact. The supply of funds is influenced by the willingness of consumers, businesses, and governments to save. The demand for funds reflects the desires of businesses, households, and governments to spend more than they take in as revenues. Usually, in very strong economic expansions, businesses’ desire to invest in plants and equipment and individuals’ desire to invest in housing tend to drive interest rates up. During periods of weak economic conditions, business and housing Investment falls and interest rates tend to decline. Such declines are often reinforced by the policies of the country’s central bank (the federal reserve in the United States), which attempts to reduce interest rates in order to stimulate housing and other interest-sensitive investments.
* The rate of inflation. People’s willingness to lend money depends partly on the Inflation rate. If prices are expected to be stable, I may be happy to lend money for a year at 4 percent because I expect to have 4 percent more purchasing power at the end of the year. But suppose the inflation rate is expected to be 10 percent. Then, all other things being equal, I will insist on a 14 percent rate on interest, ten percentage points of which compensate me for the inflation. Economist Irving Fisher pointed out this fact almost a century ago, distinguishing clearly between the real rate of interest (4 percent in the above example) and the nominal rate of interest (14 percent in the above example), which equals the real rate plus the expected inflation rate.
* The riskiness of the borrower. I am willing to lend money to my government or to my local bank (whose deposits are generally guaranteed by the government) at a lower rate than I would lend to my wastrel nephew or to my cousin’s risky new venture. The greater the risk that my loan will not be paid back in full, the larger is the interest rate i will demand to compensate me for that risk. Thus, there is a risk structure to interest rates. The greater the risk that the borrower will not repay in full, the greater is the rate of interest.
* The tax treatment of the interest. In most cases, the interest I receive from lending money is fully taxable. In certain cases, however, the interest is tax free. If I lend to my local or state government, the interest on my loan is free of both federal and state taxes. Hence, I am willing to accept a lower rate of interest on loans that have favorable tax treatment.
* The time period of the loan. In general, lenders demand a higher rate of interest for loans of longer maturity. The interest rate on a ten-year loan is usually higher than that on a one-year loan, and the rate I can get on a three-year bank certificate of deposit is generally higher than the rate on a six-month certificate of deposit. But this relationship does not always hold; to understand the reasons, it is necessary to understand the basics of bond investing.
13. Interest Rates and Discrimination
Despite laws, such as the equal credit opportunity act (ecoa), that prohibit discriminatory lending practices, systemic racism prevails in the U.S. homebuyers in predominantly black communities are offered mortgages with higher rates than homebuyers in white communities, according to a realtor.com report published in July 2020. Its analysis of 2018 and 2019 mortgage data found that the higher rates added almost $10,000 of interest over the life of a typical 30-year fixed-rate loan.
In July 2020, the consumer financial protection bureau (cfpb), which enforces the ecoa, issued a request for information seeking public comments to identify opportunities for improving what ecoa does to ensure nondiscriminatory access to credit. “Clear standards help protect African Americans and other minorities, but the cfpb must back them up with action to make sure lenders and others follow the law,” stated kathleen l. Kraninger, director of the agency.
14. Application
14.1. Simple Interest: Application
14.1.1. Car Loan
Car loans are paid monthly, which means that a part of the loan pays the remaining balance every month, and the balance portion goes toward the interest payment. As the remaining loan balance reduces every month, the interest to be paid also decreases. For example, suppose you have bought a car with a loan amount of 
300,000. 
300,000. The loan rate of interest is 5%, 5%, and the loan repayment time is 55 years. Now, using the simple interest formula, you can easily calculate the monthly EMI of it. Let us find the total interest of 55 years on the principal amount.
S.I. = P × T × R/100 ⇒ 300,000 × 5 × 5100 = 
75,000
Now, the
Amount = 
300,000 + 
75,000 = 
375,000
Thus, your Emi will be = 
375,000/(12 × 5) = 
6250
14.1.2. Certificates of Deposit
It is a type of bank investment. The Certificate of Deposit (CD) is designed to pay you out a specific amount of money on a specific date. Until that date arrives, you can’t take money out of a CD.
If you invested 
100,000
100,000 in 11 years at 3% interest yearly, the interest of 11 year on the principal amount.
S.I. = P × T × R100 ⇒ 100,000 × 12 × 3/(100 × 12) = 
3000
Now, the amount = 
100,000 + 
3000 + 
103,000
So, you will get 
3000![]()
3000 extra at the year-end.
If the CD pays the same interest rate per annum but only for three months, how much will you earn from CD?
S.I. = P × T × R100 ⇒ 100,000 × 3 × 3100 × 12 = ![]()
750
So, you will get ![]()
750![]()
750 extra after three months of investment.
14.1.3. Consumer Loan
Generally, the department stores often provide appliances on a simple-interest basis for a maximum of one year. For example, assume that you want to buy a refrigerator for ![]()
20,000 and don’t have sufficient money to buy it in cash. So, you decided to buy it in a monthly installment. The department store is giving the loan on 8% simple interest for 12 months or 1 year.
S.I. = P × T × R100 ⇒ 20,000 × 8 × 12,100 × 12 = ![]()
1600
Now, the amount = ![]()
20,000 + ![]()
1600 = ![]()
21,600
So, you will pay ![]()
1600 extra at the year-end.
So, it is concluded that if you had ![]()
20,000 then you would pay less amount instead of repaying a portion of it every month.
Currently, most banks apply compound interest to loans because it allows them to charge their customers a higher interest rate, but this method is more complex and challenging to explain [9] . Using simple interest methods, on the other hand, simplifies the calculation. Simple interest is beneficial when a customer wants a loan for a short period, such as 1 month, 2 months, or 6 months.
14.1.4. Application of Simple Interest (SI) to Find the Compound Interest (CI)
The interest accrued during the first unit of time in compound interest is added to the original principal. The amount so found is taken as the principal for the second unit of time. The amount of this principal at the end of the second unit of the time becomes the principal of the third and so on. The compound interest is the difference between the final amount and the original principal.
We will see how we could find the compound interest of a principal amount using the simple interest formula. In the table, we have taken the principal = ![]()
100 = ![]()
100 at 10%10% per annum and for 33 years.
14.2. Applications of Compound Interest
Compound interest is calculated on the principal (original amount) and the interest that has already been calculated. Each year, compound interest gets multiplied. The main applications of the formula for compound interest include its applications in solving real-world problems mathematically. The different uses of the compound-interest formula are as follows:
1) Interest compounding, not annually (monthly)
2) Deterioration and growth in the population
3) Changes and decreases in commodity prices
4) The value of the item will increase and decrease, worth of an item
5) Inflation in profits and losses
6) Bank transactions
So now, as we have discussed the applications of compound interest, we will jump upon some examples of compound interest. So, it’s all about what are the applications of compound interest.
15. Conclusions
Interest rates are a crucial aspect of modern economies, as they influence the cost of borrowing, investment, and spending decisions made by individuals, firms, and governments. The central bank, usually through its monetary policy, sets benchmark interest rates to control the supply of money [10] , maintain price stability, and support overall economic growth. In recent years, many central banks have kept interest rates low to support their economies during the COVID-19 pandemic and its associated economic downturn. This has led to lower borrowing costs for consumers and businesses, boosting spending and investment. However, low interest rates can also have drawbacks, such as potentially inflating asset prices and reducing the returns available to savers.
Interest rate changes can also have significant impacts on international capital flows, currency values, and trade balances. In general, higher interest rates in one country can attract foreign investment [11] , leading to an appreciation of its currency, while lower rates may discourage investment and lead to a depreciation of the currency.
In conclusion, interest rates are a powerful tool that central banks can use to influence economic activity, but they can also have far-reaching and sometimes unintended consequences [12] . As such, it is important for policymakers to consider all factors before making changes to interest rate policy, including the state of the economy, inflation, and financial stability risks [13] .