Interest Definition

What Is Interest?

Interest is an expense paid by a borrower for the use of borrowed money. Interest is usually expressed as a percentage of the outstanding balance of money owed to the lender, charged annually on top of the principal balance owed. Interest can also be expressed as a rate of return on an investment.

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How Interest Works

interest

The word interest came from the Medieval Latin “interesse,” which means “compensation for loss[1].”

When an individual, bank, or financial institution lends money to another party, they are hypothetically missing out on opportunities they could have made with the money they have lent out. This is called opportunity cost, and the borrower compensates the lender for it (alongside other reasons, such as risk) by paying interest. In other words, interest is the borrower’s cost of borrowing money.

There are other considerations why almost every lender charges interest. Apart from the opportunity cost, lenders also look at:

  • Risk of default (the borrower not paying the loan)
  • Inflation
  • The possibility of government intervention on interest rates
  • Length of time of the loan
  • How liquid the loan is

This is why when a borrower takes on a loan, they pay back not only the amount they have borrowed (the principal) but also the interest, expressed as an interest rate. The interest rate is a numerical representation of interest due per payment period, usually written as a percentage of the principal. These rates can be calculated using either simple interest or compound interest[2].

That said, the reverse is also true. When an individual or a business deposits money into a bank, the bank pays interest on the depositor’s money, which the latter would not be able to use. A bank or bond issuer may offer friendly interest rates to investors for access to the latter’s money. For instance, a bank will pay a small interest rate to entice a savings investor to open up an account with them. In this case, an individual earns interest—whether simple or compound—by simply depositing their money with the said bank.

Interest vs. Annual Percentage Rate (APR)

Borrowers often confuse the term “interest” with “annual percentage rate.” While both terms are used widely in the same financial field, there is a distinct difference between them.

  • Interest is the amount on top of the principal, which a borrower pays to gain access to money. This is common when using financial tools such as credit cards, mortgages, or auto loans.
  • The annual percentage rate or APR refers to the annual cost of credit or loan, which includes the interest plus additional fees attached to it. This tends to make the APR higher than the interest rate. A mortgage, for example, may require supplementary fees such as broker fees, loan origination fees, and mortgage protection insurance on top of the interest.

While it makes sense to just look at the APR when comparing rates and fees on loan products, the advantages of doing so are not always clear-cut. For example, because adjustable-rate mortgages have variable interest rates, the APR is not always representative of its maximum interest rate[3].

How to Calculate Interest

Generally, there are two ways to calculate interest: simple and compound.

Simple Interest

Simple interest is paid based only on the principal amount and not on interest payments. Home and student loans are some of the most common examples of simple interest loans.

Principal x Interest Rate x Time = Simple Interest Rate

Simple Interest + Principal = Total Amount to Pay

For instance, if a borrower borrows $80,000 at a 15% interest rate over three years, the calculation would be: ($80,000 x 0.15) x 3 = $36,000. This means the borrower would owe $36,000 in interest over the three-year loan period. When the principal amount is added, the borrower ends up paying a total of $116,000 over the loan period.

Compound Interest

Unlike simple interest, compound interest is paid not only on the principal amount but also on the interest from the previous pay period. In other words, the borrower is paying interest of the previous month—on top of interest on the principal—every payable period.

This also applies to an opposite scenario: if a person’s money earns compound interest from a bank account, this interest is regularly added to their balance. Not only does their money earn interest, but their interest earns interest as well[4].

P(1 + [r/n]) ^ nt = Total Amount Earned

where:

P: Principal
r: Annual interest rate
n: Number of compounding periods per year
t: Time in years that the money compounds

For example, a savings investor has $1,000 that earns 5% compounded monthly. After 15 years, they would have roughly $2,114. Of this amount, $1,000 represents his principal or initial deposit, while the rest is accrued interest.

Types of Interest Rates

variable interest

Borrowers may encounter different types of interest rates as they apply for a loan, particularly a mortgage. These types of rates can affect how much a borrower will pay over the life of the loan.

  • Fixed-Rate. A fixed interest rate is a pre-determined interest tied to a specific loan or line of credit that must be repaid, together with the principal. Because it is simple to calculate and understand, a fixed rate is the most common form of loan interest for customers. Lenders and borrowers know the exact rate obligations tied to the loan or credit account with a fixed-rate interest.
  • Variable-Rate. As its name implies, a variable-rate interest can change, but the monthly payments remain the same. If the prime rate increases, more of the payment is paid to the interest; if the prime rate decreases, more of the payment is instead redirected to the principal. Generally, variable-rate loans have a lower interest rate than fixed-rate loans because they are riskier to the borrower[5].
  • Adjustable-Rate. An adjustable-rate is a subtype of a variable rate. Like the latter, the interest rate changes; but unlike the variable-rate, so does the monthly payment. These adjustments happen so the borrower maintains the planned amortization schedule within the loan period. With this interest loan type, the payment decreases if the adjustable-rate interest decreases. The same goes for when the interest rate rises.

Real-World Applications of Interest Rates

Interest rates apply to different financial tools, including but not limited to:

  • Mortgages. Most mortgages utilize simple, fixed-rate interest, which means homebuyers pay equal monthly payments for the life of the loan.
  • HELs and HELOCs. A home equity loan (HEL), often referred to as a second mortgage, allows borrowers to borrow against the equity they have accumulated in their property. As with mortgages, the interest rate for HELs is set and typically remains the same throughout the loan period. On the other hand, a home equity line of credit (HELOC) lets borrowers get a line of credit from the equity they have built up in their home, which they can use for large expenses. With these, borrowers only pay interest on the amount they actually use from the borrowed money. HELOCs often use a variable-rate interest scheme. In some cases, they can also apply fixed-rate options, but these tend to have higher rates.
  • Credit cards. Taking out money on a credit card is similar to taking out a loan. If a borrower fails to repay the expected amount of money in a given period, the amount of interest will increase. The interest rate may depend on several factors, including the borrower’s creditworthiness, primarily because a credit score is analyzed before approving an individual for a line of credit.

Other financial tools where interest rates apply include auto loans, business loans, student loans, and certificates of deposits (CDs). Naturally, each of these instruments will have its own classification of interest rates.

How Are Interest Rates Determined?

interest federal reserve

Interest rates are based on three important economic and financial factors:

The Federal Reserve

The Federal Reserve sets the federal funds rate, or the short-term interest that banks and other institutions charge each other overnight. They have the biggest impact on interest rates mainly because the federal government tasks them to balance rates at a level where prices are stable, and liquidity within the national economy is abundant. As a result, it triggers changes in other interest rates, such as mortgages and credit cards, and influences the foreign exchange rate of the U.S. dollar—which, in turn, dictates prices of assets and commodities in the market[6].

When interest rates are low, economic activity is spurred. People tend to spend and loan more, real estate prices rise due to an influx of buyers, and businesses grow as a result of extra capital. On the contrary, higher interest rates mean the burden for loaning money is heavier, leaving the borrower with fewer savings. Eventually, this results in slow economic activity.

U.S. Treasury Notes and Bonds

Bonds and interest have a negative relationship[7], which means as the cost of bonds increase, the interest rate falls, and vice versa. Demand for U.S. Treasury notes and bills affects longer-term and fixed-rate interests on credits and loans, particularly in the fixed-income investment market.

Banks

To stay afloat in a highly competitive market, banks must compromise between making decent rates for loans and keeping rates attractive enough to earn the business of borrowers and savings investors. And because they operate in close range across the entire sector, banks provide borrowers, investors, and financial institutions with a good idea of where interest rates are at a given time, across a range of rates.

Takeaways

Borrowing money does not come free, whether it is borrowed from a bank or an individual lender. If an individual takes out a loan to buy a house, purchase a new vehicle or start a business, they will almost always have to pay interest to the lender for giving them access to money. At the same time, the reverse is true: individuals can earn interest from banks by depositing their money and doing business with said institutions.

Paying off a loan starts with understanding how interest is tacked onto the principal amount. It can either be simple or compound and can be further classified as fixed, adjustable, or variable. Knowing how much interest they are paying over time can help them find lower rates or pay off debt much faster, and more awareness of how the economy uses interest rates as one of its bases can help borrowers plan healthier borrowing habits.

Sources

  1. Online Etymology Dictionary. (n.d.) Interest. Retrieved from https://www.etymonline.com/word/interest
  2. Black, M. (2021.) How to calculate loan interest. Bankrate. Retrieved from https://www.bankrate.com/loans/personal-loans/how-to-calculate-loan-interest/
  3. Consumer Financial Protection Bureau. (2019.) What is the difference between a mortgage interest rate and an APR? Retrieved from https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/
  4. Pritchard J. (2020.) How Compound Interest Works and How to Calculate It. The Balance. Retrieved from https://www.thebalance.com/compound-interest-4061154
  5. Wamala, Y. (2021.) Fixed vs. Variable Interest Rates: What’s the Difference? ValuePenguin. Retrieved from https://www.valuepenguin.com/loans/fixed-vs-variable-interest-rates
  6. Federal Reserve Bank of Chicago. (n.d.) The Federal Funds Rate. Retrieved from https://www.chicagofed.org/research/dual-mandate/the-federal-funds-rate
  7. Lioudis, N. (2020.) The Inverse Relationship Between Interest Rates and Bond Prices. Investopedia. Retrieved from https://www.investopedia.com/ask/answers/why-interest-rates-have-inverse-relationship-bond-prices/

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