Albert Einstein described compound interest as “The most powerful force in the Universe.” But what exactly is compound interest, anyway? And how does it differ from simple interest?

Simple Interest vs Compound Interest Formulas

The Simple Interest Formula

  • Simple Interest = P x R x N

The Compound Interest Formula

  • Compound Interest = P × (1+r)−P

What is Interest?

Interest is the cost of borrowing money or what you charge to loan money. You probably know about interest on your credit cards, student loans, car loan, and mortgage. The interest payments associated with these monthly expenses come from the fact that financial institutions, like banks and lenders, have given you money or credit to buy things you want and/or need. If they didn’t charge interest for loaning that money, they’d be out of business. Interest charges provide motivation for lenders to extend credit to borrowers.

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Earned Interest Defined

Interest can also have a positive connotation. Banks pay you interest for placing your money into their care. They take that money and lend it out to homebuyers, business owners, and even corporations. The bank earns interest on this money, which they use to cover their costs and pay out profits to shareholders, as well as interest payments to those who have placed deposits in the bank’s care.

These interest payments vary from bank to bank and account type to account type. Checking accounts typically offer the lowest interest payments, if any, followed by savings accounts, money market funds, and CDs. Some banks offer clients with a certain amount of equity in the bank tiered rewards, like improved interest rates. Interest rates can also vary with the economy and political climate.

The government pays you interest when you buy treasury bills, notes, or bonds. If you wait until your bond fully matures, you can cash it out for its maximum value—though you can cash it out at any time for less. This is the government’s way of paying interest on the money loaned to it. The interest rates on these notes vary, and they are offered by federal, state, and even municipal governments.

Another way to earn “interest” is through investments, although this would more accurately be described as growth. CAGR or compound annual growth rate is a useful metric for seeing how much an investment, like a stock portfolio, will grow over time, by giving you the annual rate of return. Your stock portfolio will “compound” because the percentage of growth is applied to the real time value of your portfolio. So, if you put more money into it every month, you’ll be earning on that money as the value grow.

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What is Simple Interest?

Simple interest is applied to the principal borrowed and multiplied by the loan term. This is typically calculated in terms of years. If a loan lasts more than a year, then it’s probably not going to be a simple interest loan. Rather, the lender will charge you for the initial loan amount and any unpaid interest. This is called compound interest, and its terms are better for the lender. There’s no harm in learning how structuring a loan or a deal can bring about the most benefits, especially if you want to know how to make a million dollars.

What is Compound Interest?

Compound interest is applied both to the principal and the interest that has accrued so far.  Essentially, the borrower is paying interest on the interest. If this sounds like a bad deal, that’s because it is! Unfortunately, beggars can’t be choosers, and if this is the only type of loan you’re able to secure, then so be it.

As much as you are able to, this is why it’s important to understand the difference between simple vs compound interest and shop around for the best loan terms possible. There are many Qualified Retirement Plans that offer compound Interest which helps your money grow faster than a simple interest account.

The Differences Between Simple and Compound Interest

The main difference between simple and compound interest is that simple interest will only have you (the borrower) paying interest on the principal, while compound interest will have you paying interest on the interest. Simple interest provides better loan terms for the borrower, while compound interest is a sweet deal for the lender.

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Another important point is that even simple interest will be recalculated periodically. So, periodically, unpaid interest on a loan becomes part of the new loan amount. Many financial advisors will tell you to make payments above and beyond monthly minimums, so you can knock out the interest that has been applied to the loan amount.

This may not be reflected in the total, though. For instance, assume you have a credit card balance of $5,000, with an APR of 20 percent (not a good rate). But the card issuer only charges you a monthly payment of one percent of the total balance. This is rather misleading because you probably think if you only pay $50 per month, you will chip away at your balance.

The sad truth is that it would be like chipping away at a mountain with a toothpick, because every month the bank is adding more unpaid interest to your balance. Instead, ask the bank about the compounding period. Better yet, just look at your bill for the interest charge. Pay your monthly minimum and the interest charge so the debt doesn’t snowball.

Unfortunately, many consumers are not educated about these financial issues, but the more investing books and personal finance articles you read, the better equipped you will be to avoid debt traps.

Simple Interest vs Compound Interest Formulas

Simple Interest Formula

The formula for simple interest is as follows:

Simple Interest = P x R x N

P represents the principal amount of money borrowed or lent (depending on who you are), while the R represents the annual interest rate, and N represents the term of the loan in years.

If for whatever reason, the interest rate is applied monthly, that loan term can also be represented in months. And if the interest rate is annual and the loan is less than a year, that number can be illustrated as a number or a fraction.

Compound Interest Formula

The formula for compound interest is more complex:

Compound Interest = P × (1+r)−P

In this formula, P represents the principal amount, R, once again, represents the annual interest rate, and the exponent t represents the number of years this interest will be applied.

Examples of Simple Interest

A simple interest loan is typically a short term or smaller loan, like a personal loan or car loan. In the United States, some mortgages are also included among simple interest loans, but others are not. Sometimes the accrued interest one earns on a CD is also simple interest.

For this example, we’ll use a CD. Let’s say you make a fixed deposit to your bank of $10,000, placing it into a CD with a one percent rate of growth. The principal balance is $10,000. The simple interest rate is one percent.

P x R x N = Simple Interest

$10,000 x .01 x 1 = $100.

This means that the interest payment your bank will pay you is $100 after one year. Banks usually express this number (in percentage form) as an Annual Percentage Yield or APY, rather than an Annual Percentage Rate or APR, which refers to the interest charge the borrower pays the lender.

In this case, the bank is paying you money. However, if you are going to deposit your money into something like a CD for more than one year, you would want it to be earning compounding interest.

Examples of Compound Interest

Let’s say you take the same $10,000 as the original amount and put it into a 5-year CD with compounded interest. Let’s even say that the compound interest rate is the same as the aforementioned one percent. In this case…

P x (1+r)− P = Compound Interest

$10,000 x (1 + 0.01)5 – $10.000 = $510.10

As it turns out, the compounding period for many CDs is monthly, which is good news, but also necessitates a different formula. For the sake of simplicity, we’ll leave our current example with an annual compounding period.

As a general rule of thumb, before signing anything to accept a loan, such as a student loan or business loan, you should find out if you’re going to pay interest on the accumulated interest and use a compound interest calculator applicable to that situation. Make sure that the lender gives you the financial modeling of a concrete number that will represent the total amount of your monthly payment. You never want to be in a situation with a compound interest loan that feels like a sandpit you can’t climb out of.

Speaking of which, it’s important to know that even the best credit card in terms of points probably charges compound interest—daily—on the balance. That’s how they get you, as the saying goes.

It’s Important to Know the Difference Between Compound Interest and Simple Interest, Especially When Borrowing Money

Compound interest is a powerful force. When it’s applied to money you owe, the effect can be devastating, but one you can avoid if you make sure you are paying your monthly minimum payment and the interest owed. But when compound interest is applied in your favor, such as with a growing brokerage account you make regular contributions to, the effect is wonderful.

If you want to learn more about making your money work for you, including the best investment accounts and borrowing strategies, sign up for a free Infinity Investing Membership. Our experts, tools, and resources will guide you down the path to financial freedom, providing wealth and security for many years to come.

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Infinity Investing Featured Event

In this FREE event you’ll discover how the top 1% use little-known “compounders” to grow & protect their reserves. Our Infinity team of experts show you how to be the best possible steward of your finances and how to make your money and investments work for you instead of you working for them. Regardless of your financial situation today, you’ll have a road map to get to where you want to be.