Simple vs. Complex Interest: Key Differences

When it comes to the world of finance, numbers reign supreme. You can’t argue with the numbers — and it is the numbers that determine outcomes of money actions. Interest rates are perhaps the most important number to understand when handling your finances.

You should be aware of two main kinds of interest: simple and compound interest. While both are types of interest, they can result in very different outcomes.

Take a look at these critical differences between simple and compound interest so that you can make intelligent financial decisions in the future.

What is interest?

Before we can get too deep into the subject, we must first cover the basics of interest. Interest is typically defined as the cost of borrowing money, but it can also be explained as the rate paid on money on deposit in cases where your money earns interest.

When you borrow money, it costs you more than the total loan amount. Your lenders expect you to pay back accumulated interest on the loan, typically calculated as a percentage.

While simple and compound interest are relatively basic financial concepts, most people are unaware of the differences. Depending on the loan terms and the type of interest, the total interest payable can change dramatically.

What is simple interest?

Simple interest is an interest rate calculated based on the principal amount of the loan and that amount only. Simple interest rates are used by financial institutions as the marketed APR (annual percentage rate) and have significant differences from compound interest.

The basic simple interest formula is: Simple Interest = P x i x n

P is the principal, i is the interest rate, and n is the term of the loan (typically the number of years). We could also write the formula as Simple Interest = Principal x Interest Rate x Time.

Simple interest is fantastic because it is effortless to calculate; it only requires some simple multiplication.

For example, if you take out a $20,000 loan at a 5% annual simple interest rate with a term of five years, you would pay a total of $25,000. That amount is from the $20,000 principal plus one thousand dollars in interest every year for five years.

What is compound interest?

Compound interest rates don’t just consider the principal of the loan when calculating interest but also the interest that has accrued so far. You can think about compound interest as earning interest on the amount of interest that has accrued, not just the principal alone.

The compound interest formula is: Compound Interest = (P(1+i)n)−P

“P” is the principal, “i” is the annual interest rate, and “n” is the number of compounding periods per year.

However, if the number of compounding periods per year is greater than one, you need to adjust your “i” and “n” values.

The interest must be divided by the compounding periods, and “n” must be multiplied by “t,” the term of the loan, to be used in the equation.

Using our example from earlier and calculating compound interest, let’s take the same $20,000 loan at 5% interest for five years, and now let’s assume quarterly compounding (or four times per year). In this case, the interest value you will use is .05%/4, and the compounding period’s value will be 20.

Now, instead of paying $25,000 over the life of the loan, you will owe a total of $25,640.

What is a compounding period?

A compounding period is the number of times per year the interest compounds on a loan or investment. If the interest compounds annually, then the compounding period is one. If the frequency of compounding is quarterly, then the compounding period is three.

The more compounding periods in a year, the faster the interest will increase over time. This is because you are calculating the additional interest based on a higher principal that frequently includes more of your interest.

Be aware of the compounding periods available, as a higher interest rate that compounds less frequently could be smarter than a lower interest rate compounding more frequently.

The key difference between compound interest and simple interest

Now that you have the basic idea of compound interest and simple interest sorted, you must understand the crucial differences between the two. Though they may seem similar, they can lead to wildly different outcomes.

Fixed growth vs. exponential growth

The first and most significant difference between compound interest and simple interest is that simple interest will give you fixed growth. In contrast, compound interest gives you the opportunity for exponential growth.

When dealing with a simple interest rate, you will notice that the growth stays constant at a portion of the principal each year, giving you the same interest payment every year for the duration of the loan.

With compound interest, however, you are paying interest on both the principal and accrued interest. As interest increases over time, so will each additional interest payment you owe.

This means that the interest can balloon quickly, especially if the interest rate is high and the compounding period is frequent. This can lead to the exponential growth of your interest and is something you should keep in mind.

When will I earn simple interest vs. compound interest?

Both simple and compound interest are common across financial sectors and institutions, giving you a multitude of different investments and loans offering both options. Here is a look at some typical times when you might encounter simple interest or compound interest.

Simple interest earning

Certificates of deposit: A Certificate of Deposit, or CD, is a financial instrument sold by banks that offers simple interest. When you purchase a CD, you are giving the bank a certain amount of money for a set period of time, with a given simple interest rate. CDs often offer higher interest rates than a savings account and can be a good option, giving your initial investment a higher annual percentage yield.
Car loans: Car loans are traditionally amortized loans, meaning that your monthly payment goes partially toward the principal and the interest. Over time, as you continue to pay the loan, the interest payable decreases, meaning more of your payment goes toward your principal.
Common consumer loans: If you have ever used a payment plan from a retailer to purchase expensive items, then you have taken out a simple interest loan. These loans are often more accessible for consumers to understand at face value.
Mortgages: Your mortgage payment and loan are also simple interest-earning loans. This is important as you usually borrow 80% or more of the value of your home. Compounding interest on such a high balance would make homeownership untenable for most people.
Student loans: Finally, student loans are typically simple interest-earning loans, and all government student loans are simple interest-earning loans.

Compound interest earning

Credit cards: When you leave purchases hanging around on your credit card, you are building compound interest. This means you pay interest monthly, not just on the cost of goods purchased with your card but on all the interest accrued so far. Compound interest is one primary reason that credit card debt is so common.
Investing: When you invest in the stock market, ETFs, Mutual Funds, and whatever other types of investments, you can earn compound interest. As the value of your investment increases over time, it compounds, especially if you reinvest dividend payments.

How to use compounding interest in your favor

While compound interest might sound scary, it can be a very powerful tool for growing your wealth. Compound interest grows faster than simple interest, so you should maximize your returns by investing in instruments that offer compounding interest.

You can also use compounding interest in your favor by paying off your principal on your loans and debts early. This lowers the remaining balance, thus decreasing the amount you owe in interest, including over time.

Paying off a compounding debt in two half payments rather than one full payment can cut your total interest by thousands of dollars in the long run.

You should also do your best to avoid falling behind on payments for your compounding interest debts, as these can snowball much faster than simple interest payments. You can use simple and compound interest to maximize your finances by making intelligent decisions.

Simple vs. compound interest: the bottom line

Simple and compound interests are not that different. The significant difference is that simple interest only occurs on balance, while compound interest accrues on both the balance and the interest accrued thus far.

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