Couple looking at personal finances, compound interest.

What Is Compound Interest And How Is It Calculated?

Kevin Graham7-minute read

December 07, 2020

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If you’re looking to buy or refinance a home, one of the key factors to understand is how much interest you’ll pay over time and how it’s calculated. For mortgages and many other loans and investments, in order to calculate this, you need to understand the concept of compound interest.

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What Is Compound Interest?

Compound interest is calculated both on the original loan balance and accumulated previous interest from prior calculation time frames. This is a very common way to calculate interest on mortgages and other loans, but also on various types of investments.

When thinking about compound interest, the important thing to realize is that it’s earned or paid on existing interest. This interest is added back into the existing balance on the investment or loan. In this way, the amount you earn or owe grows over time.

Simple Interest Vs. Compound Interest

Simple interest is calculated only on the original loan balance. Therefore, the amount earned or paid on interest doesn’t grow over time based on previous interest paid. Interest growth is slower.

By contrast, compound interest adds back previous interest charges or payments. Interest grows faster relative to the balance of the loan.

It doesn’t work this way, but from a consumer perspective, if you’re paying interest on a loan, it’s more advantageous to pay based on simple interest because the existing interest charged isn’t added back into the balance for future calculations. If you have an investment, you want it to use compound interest because adding existing interest will help your earnings rise.

Key Variables For Compound Interest

There are several factors that determine the amount paid or earned when it comes to compound interest. Let’s run through them:

  • Interest: The higher your interest rate, the more you’re going to owe on a loan or earn on an investment over time.

  • Initial principal amount: The initial amount of the loan balance or investment helps dictate how much interest is paid. The higher the principal, the higher the compound interest is going to end up being.

  • Compounding frequency: Compounding frequency can be important because the more your interest is scheduled to compound, the more interest you can earn or end up having to pay. The reasoning is the new interest amount is always added to the balance from the previous compounding calculation. The more the calculation is done, the bigger the ending balance.

  • Length of time: Because compound interest is generally all about time, the longer you keep money in the account or have a loan, the more interest is going to be associated with that.

  • Amount of deposits or withdrawals and payments: If you make deposits into an account for an investment, you’ll learn more in interest over time because the balance on which the interest is calculated is increasing. By contrast, if you make a withdrawal on an account or a payment on a loan, less interest will accumulate because the balance is smaller.

The Compound Interest Formula

When calculating how much you’ll end up making due to compound interest, there’s a formula you can use.

Compound interest formula.

  • B: Ending balance
  • P: Initial principal
  • R: Annual interest rate
  • N: Number of times each year that the interest on an investment or loan compounds
  • T: Length of time you’ll have the investment or loan

Let’s do a couple of examples to show how this works.

Let’s say you invest $4,000 in a certificate of deposit (CD) that pays 2% interest compounded semiannually (every 6 months) for 4 years. Your total return would be the following:

Example of compound interest formula in use.

In this case, when the CD matures, you’d have $4,331.43.

What if you’re trying to figure out how much interest you pay on something like a mortgage? You can use this formula to determine how much interest you would pay over the life of the loan by first getting the total amount of money paid over the life of the loan if every payment was made on schedule. Then you can subtract the initial principal balance in order to get the interest paid.

This is slightly complicated by the fact that the principal has to be reduced every month by your initial mortgage balance, so it can be easier to use a mortgage amortization calculator.

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When Compound Interest Can Help You

When the compound interest is being added to an investment, it can be helpful. While that’s the short version, here are a few examples:

  • Bank accounts: Deposits to bank accounts, whether they be checking or savings accounts or CDs, increase the balance tied to that account and thus the amount of interest earned on the investment, growing your return.

  • Investment accounts: The same compounding principle can apply to portions of other investment accounts that earn a fixed, compounding return. These would include any portions of your 401(k) that are in money market funds, for example, or CDs. Portions of your retirement or other accounts that are tied to stocks or bonds may have more variable returns.

When Compound Interest Can Be Harmful

When it’s an investment, compound interest acts as the wind at your back. When we talk about debt, compound interest works in the other direction.

  • Loans: Student loans, personal loans and mortgages all tend to calculate interest based on a compounding formula. Mortgages often compound interest daily. With that in mind, the longer you have a loan, the more interest you’re going to pay.

  • Credit cards: If you pay off your balance each month, you won’t pay any credit card interest. If you do have a balance on your card, it can be compounded. Additionally, there may be penalty rates you’re subject to if you make a late payment, so it’s important to understand what you’re signing up for and be careful with credit cards.

Advice For Making Compound Interest Work For You

There are ways that you can make compound interest work to your advantage. Here are a few of them:

  • If you’re making an investment, do so early and make regular deposits so that the balance in the account can grow over time. This is especially true if the account pays compounding interest.

  • On your debts, it’s important to remember that compound interest builds up the longer the loan lasts. In some instances, it may even compound daily. This is why you can save so much money on interest if you pay off the balance on your mortgage early.

  • When dealing in compound interest, you may find it useful to compare using the annual percentage yield (APY). APY takes into account compounding interest. By contrast, annual percentage rate (APR) is based on a simple interest formula that doesn’t compound payments. The one exception to this tends to be mortgages because they tend to be higher closing costs involved which are included in the APR. For this reason, APR tends to be a more accurate representation in this area.

  • If given the option, you want your investments to compound on a more frequent basis and loans to compound much less frequently if at all. Unfortunately, you’re not always given the option. However, one thing you can control is how long it takes you to pay off your debt. Just make sure there’s no prepayment penalty associated with your loan.

Bottom Line

One of the simplest ways to think of compound interest is that it’s earned on already-existing interest. Basically, the more frequently interest compounds, the more interest is generated as previous interest payments are added to generate a higher principal balance. Given this, you want compound interest on investments. It’s to your disadvantage on debts.

In contrast to compound interest which is calculated again every time the interest is scheduled to compound, simple interest is only calculated based on the original principal balance.

There are several variables that impact the amount of compound interest generated by an investment or loan. These are the initial principal balance, the annual interest rate, how frequently the compounding is to take place and the length of time you have the investment – usually measured in years. You can use the compounding formula to determine your return on investment or to compare the interest associated with different types of loans.

As a general rule, compounding interest on investments like bank accounts and CDs is good. It’s less desirable on debts like student loans, mortgages and personal loans.

To take the fullest advantage of the way compound interest works, invest early and often in accounts offering compounded interest. On the other hand, pay off any debts as quickly as possible because time is one of the most important factors in compound interest calculations. You’ll also want to look at APR or APY for an accurate view of interest charges, depending on the type of account or loan being opened.

If you’re ready to buy or refinance a home now that you understand more about the way interest works, get started online. You can also check out more on our Rocket Mortgage® Learning Center.

Take the first step toward the right mortgage.

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Kevin Graham

Kevin Graham is a Senior Blog Writer for Quicken Loans. He specializes in economics, mortgage qualification and personal finance topics. As someone with cerebral palsy spastic quadriplegia that requires the use of a wheelchair, he also takes on articles around modifying your home for physical challenges and smart home tech. Kevin has a BA in Journalism from Oakland University. Prior to joining Quicken Loans, he freelanced for various newspapers in the Metro Detroit area.