What is Compound Interest?

Discover what compound interest is and how it can affect your banking strategy

In 1790, to illustrate the 'magic' of compound interest, Benjamin Franklin bequeathed $5,000 each to the cities of Boston and Philadelphia. Two hundred years later, the two Benjamin Franklin funds were valued at a combined $6 million. Though this return might seem high for a $10,000 investment, an understanding of compound interest will help demonstrate how it came to be. In this guide, you'll learn the definition of compound interest, how to calculate it and the perks of investing in an interest-bearing account.

The benefits of investing in an account with compound interest vs. simple interest

A simplified compound interest definition is 'earning interest on interest.' In simple-interest investments, the return is derived from the original principal, while compound-interest investments recalculate the principal at the end of each compounding period. At that point, any accrued interest is added to the principal, and the new, higher principal will accumulate interest until the end of that compounding period when the principal is recalculated once again.

When it comes to simple interest vs. compound interest, the basic difference is that compound-interest accounts will continue earning higher and higher returns throughout the length of the investment, whereas simple-interest accounts will always have the same return (assuming there are no additional contributions to the investment). Here's a quick rundown of a few key principles of compound-interest investments:

  • Compound-interest investments continue to work for you - The most enticing aspect of compound interest is that your initial investment will continue to generate increasingly higher returns. Even if you never add to your initial investment, you'll continue to see higher yields.

  • Time is the most important factor - Compound interest can lead to significant returns for investors of all financial situations, not just savvy financiers. With compound interest, when you start saving is just as significant as how much you save. The more compounding periods your investment completes, the more you can expect to see your money grow.

  • Many diverse accounts use compound interest - Most deposit accounts, such as personal savings accounts, money markets and certificates of deposit (CDs), use compound interest. Additionally, retirement accounts such as 401(k)s and IRAs also calculate returns using compound interest.

Learn the process for calculating compound interest

Though it might seem like a complicated formula, calculating compound interest is pretty straightforward when you understand what each letter in the following formula signifies:

FV = PV ( 1 + r/n )nt

  • PV - PV stands for 'present value' and should be replaced with your current principal or account balance.

  • FV - FV is the variable that you're calculating and represents the 'future value' of your investment.

  • r - Replace r with your compounding interest rate written as a decimal. For example, if your rate is 1.5% APY, replace r with .015 when calculating.

  • n - Use the number of compounding periods per year for n.

  • t - Plug in the time (in years) that you'll keep your money in the account.

As an example, let's say that you have $2,000 that you invest at a 5% interest rate, for one year, in an account that compounds annually:

  1. Since we are calculating for what the future value (FV) will be, we know that the present value (PV) is 2000.

  2. The interest rate was said to be 5%, so replace r with .05.

  3. For the sake of this example, we're only investing the principal for one year, so replace t with 1.

  4. Since the interest compounds annually, n will also be 1.

  5. Once you plug in all the values, your equation will be: FV = 2000 ( 1 + .05/1 )1(1)

  6. Solve the equation and you'll find that FV comes out to 2100, which means that for leaving your money in this interest-bearing account for one year, you'll earn $100 in interest. For each year you keep the money in the account, the amount of interest you receive at the end of a compounding period will increase.

Now, let's leave the $2,100 from the previous example in the same account, at a 5% interest rate, for two additional years:

  1. The new PV will be 2100 since that was the value of our investment at the end of the first year.

  2. The interest rate is still 5%, so r is .05.

  3. The investment period for this example is 2 years; therefore, t will be 2.

  4. The interest compounds annually, so n is 1.

  5. Plug in the values and your equation will be: FV = 2100 ( 1 + .05/1 )1(2)

  6. After solving this equation, FV is 2315.25. This means that, for leaving your $2,000 in this account for three years, you earn $315. It's also important to keep in mind that, in this example, there were no additional deposits to the account. If possible, investors will likely make monthly contributions to accounts with compounding interest so that they grow more quickly.

Take advantage of compound interest with a Citizens Bank savings account

Now that you know what compound interest is and are familiar with the benefits of having interest-bearing accounts, you can start investing your money in a savings account from Citizens Bank. To choose an interest-bearing account, compare savings account interest rates to find the best option for your goals. By comparing rates, you'll be able to pick an account with a competitive rate to grow your savings quickly.

To learn more about compound interest or about any of our deposit accounts, contact a Citizens Bank customer service representative today.


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