What Is Compound Interest And How Is It Calculated?
Andrew Dehan9-minute read
November 21, 2022
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.
Compound interest is interest calculated based on the initial principal and appreciated interest from the previous period. Learn more about how to calculate compound interest and the benefits and disadvantages of compound interest for your investments.
- Compound interest is the interest you earn based on your original amount of money and the accumulated interest.
- Compound interest is determined by multiplying the initial principal by one plus the interest rate raised to the number of total compound periods minus one.
- The earlier you start investing with compound interest, the more you will earn in your lifetime.
Table Of Contents
What Is Compound Interest?
Compound interest is calculated both on the original loan balance and from previously accumulated interest from prior calculation time frames. This is a very common way to calculate interest on mortgages and other loans, as well as 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 increase.
How To Calculate Compound Interest
Compound Interest Formula
B = P x (1 + R/N)(N x T)
Let’s break down this formula by each of its components:
- 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
Here are a couple of examples to show how this works.
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:
Compound Interest Calculation Example
$4,000 x ( 1 + .02/2)2x4
Ending balance: $4,331.43
In this case, when the CD matures, you’d have $4,331.43.
Now, 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 if every payment was made on schedule. Then you can subtract the initial principal balance 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 taking a careful look at how mortgage amortization is calculated will be important.
5 Factors That Influence Compound Interest
- 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. This is because 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 it.
- Amount of deposits or withdrawals and payments: If you make deposits into an account for an investment, you’ll earn 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.
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When Compound Interest Can Help You
- Bank accounts: Deposits to bank accounts, whether they’re 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 or CDs, for example. Portions of your retirement or other accounts that are tied to stocks or bonds may have more variable investment.
- Stocks: A stock is a small share of ownership of a corporation. Owning stocks that pay dividends will generate compound interest if you reinvest the dividends into more dividend-earning shares. The stock market is volatile, so it’s important to keep an eye on your investments and choose stocks that have a relatively stable price to avoid sudden drops.
- Mutual funds: A mutual fund is a professional investment program shared between shareholders. Mutual funds typically invest in securities like bonds and stocks.
- Real estate investment trusts (REITs): REITs are groups that invest and own income-producing real estate, like apartment complexes, retail centers and offices. REITs that offer dividend reinvestment options will allow you to benefit from compound interest.
To learn more about investing your money in real estate and other investments, check out some of our investing book recommendations.
When Compound Interest Can Be Harmful
- Loans: You’ll typically see compound interest with personal and student loans. 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.
How To Make Compound Interest Work For You
- Make regular deposits. If you’re investing, 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.
- Try to pay off your mortgage early. With 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 your mortgage early.
- Compare compound interest using APY and APR. 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 is mortgages, because they tend to include higher closing costs. When comparing APR versus interest rate alone, APR tends to be a more well-rounded look at what you’ll pay for your mortgage.
- Ensure there’s no prepayment penalties on debts. If given the option, you want your investments to compound on a more frequent basis – meaning the compounding period would be shorter – and loans to compound 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.
What Are The Pros And Cons Of Compound Interest?
Let’s take a look at the benefits of a loan with compound interest.
- Build your savings faster: If you invest in a stock or bond with compound interest, you’ll see your initial investment grow quicker compared to just earning simple interest. Not only will you earn returns on the money you’ve invested, but you will receive returns at the end of the compounded period. With compounding, there’s an exponential growth because both your original amount and growing income are compounded.
- It’s free: With an investment, the compound interest is typically included free of charge. You don’t need to pay extra to see your investment grow at a quicker rate.
- Time is your benefit: Time is key with compound interest. The earlier you add money into your investment, the more income you’ll see being generated. Both your initial investment amount and interest rate will determine how quick your new income accumulates. The longer you keep adding money to your investment account, the more you’ll see down the road.
Although there are great benefits to compound interest, there can be disadvantages you should be aware of when investing.
- Fees are involved: Although you don’t need to pay a fee for compound interest, there’s always fees that occur to invest. Fees that may occur include commissions, expense ratios, annual and custodian fees, and loads. These will affect how quickly your investment grows. Plus, most interest is considered taxable, so make sure to check with a tax advisor to find out if you need to pay income tax on all of your compounded interest earned each year.
- Can be more harmful than good: If you’re dealing with compound interest debt, such as student loans or credit card debt, it can work against you. For example, many credit card companies utilize a daily compounding fee that’s added to your total debt when it’s not paid off month over month. Therefore, you’ll typically need to pay back more than your initial credit use.
- Patience is key: With compound interest, time is in your favor. However, this means you won’t see large returns on your initial investments when you first start. Plus, how large your returns are will depend on the amount you invest. If it’s a small amount, it will take more time to see growth versus a larger amount. Adding funds to the investment account over time will help grow your income.
Compound Interest FAQ
When looking at your investment account or credit card, it’s easy to spot whether you’re dealing with simple or compound interest. With compound interest, you’ll see the interest per period is based on your principal balance and any interest that’s already accumulated.
With simple interest, it should only be based on your principal balance. For example, you should only see simple interest occur with a home equity line of credit. However, with credit card debt, you will typically see a compound interest.
The Bottom Line: Work With Compound Interest, Not Against It
One of the simplest ways to think of compound interest is that it’s earned on already-existing interest. The more frequently the interest compounds, the more interest is generated as previous interest payments are added to generate a higher principal balance. You want compound interest on investments, but not on your debts.
Compound interest is calculated again every time the interest is scheduled to compound, whereas simple interest is only calculated based on the original principal balance.
Several variables that impact the amount of compound interest generated by an investment or loan include 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.
To take fullest advantage of the way compound interest works, invest early and often in accounts offering compounded interest. On the other hand, you should pay off any debts as quickly as possible because time is one of the most important factors in compound interest calculations.
Hoping to find a way to buy a home and get the lowest possible interest rate? Read more about how to find the best mortgage rate so you can enter the home buying process fully prepared.
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