Interest Rate , Formula, & Calculation

What Is an Interest Rate?

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.

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.

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. 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.

Risk is typically assessed when a lender looks at a potential borrower's credit score, which is why it's important to have an excellent one if you want to qualify for the best loans.

Interest Rate Example

If you take out a $300,000 mortgage from the bank and the loan agreement stipulates that the interest rate on the loan is 4%, this means that you will have to pay the bank the original loan amount of $300,000 + (4% x $300,000) = $300,000 + $12,000 = $312,000.

Simple Interest Rate

The example above was calculated based on the annual simple interest formula, which is:

Simple interest = principal X interest rate X time

The individual that took out a mortgage 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 for 30 years, the interest payment will be:

Simple interest = $300,000 X 4% X 30 = $360,000

An annual interest rate of 4% translates into an annual interest payment of $12,000. After 30 years, the borrower would have made $12,000 x 30 years = $360,000 in interest payments, which explains how banks make their money.

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 to the principal but also on the accumulated interest of 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. 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:

Compound interest = p X [(1 + interest rate)n − 1]
where:
p = principal
n = number of compounding periods

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.

The snowballing effect of compounding interest rates, even when rates are at rock bottom, can help you build wealth over time; Investopedia Academy's Personal Finance for Grads course teaches how to grow a nest egg and make wealth last.

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.

APR vs. APY

Interest rates on consumer loans are typically quoted as the annual percentage 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.

How Are Interest Rates Determined?

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 (the Federal Reserve in the U.S.) sets the interest rate, which each bank use to determine the APR range they offer. When the central bank sets interest rates at a high level, the cost of debt rises. 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. 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.

The average interest rate on a 30-year fixed-rate mortgage in June 2021. The Federal Reserve has not cut back on its increased spend on mortgage-backed securities, which keeps mortgage rates low.

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.