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How Does Compound Interest Work?

A woman researches how compound interest works on her laptop.

You've likely heard that compound interest can help boost your retirement savings. But how does compound interest work, exactly?

Financial institutions offer different types of interest that can be used to calculate the amount of money you earn on a deposit. Compound interest is one type of interest, and it can help you grow your money over time. To help you better understand compound interest, here's some information on how it works and how it can help boost your retirement savings.

What Is Compound Interest?

Compound interest multiplies the interest rate by your principal balance plus the amount of interest that's already accrued in your account. For that reason, compound interest is sometimes referred to as earning "interest on interest."

Say, for example, that a customer has $10,000 in a retirement savings account and the financial institution offers a 2% interest rate. If the financial institution compounds interest once a year, the account would accrue $200 in the first year ($10,000 x 0.02). But in the second year, you would receive an interest credit of $204. That's because the financial institution is multiplying its 2% rate by $10,200, which is the amount of the initial deposit plus the previous year's interest.

How Does Compound Interest Work?

In the previous example, the extra $4 generated by using compound interest may not sound like much of a difference. But the key to compounding is that the effect becomes larger over time.

Assuming the customer above does not make any additional deposits or withdrawals, that same account would be worth $12,190 in 10 years if the interest is compounded yearly. And by year 20, its value would jump to $14,859.

How to Calculate Compound Interest

The amount of interest built up through the compounding method is a function of the interest rate, the frequency with which the financial institution compounds the interest, and the length of time the money is left in an interest-bearing account. The formula for compound interest looks like this:

A = P(1+r/n)nt

In the above formula:

  • A = ending balance
  • P = principal amount
  • r = nominal (stated) interest rate
  • n = number of times interest is compounded per year
  • t = number of years money is left in account

Examples of How Compound Interest Works

Let's apply this formula to the example mentioned earlier, supposing that the customer left a $10,000 principal balance in their savings account. "R" is 0.02, which represents the 2% annual rate. If interest only compounds once a year, we'd divide that rate by 1, which represents the once-a-year compounding method. To determine the account balance after 10 years, we'd multiple 1 (our compounding frequency) by 10. The result is an ending balance of $12,190.

One of the important aspects of this formula is that "n" — the number of compounding periods in a given year — is part of the exponent. As a result, the more frequently a financial institution performs compounding, the greater the amount of interest you'll earn from the very same stated interest rate.

To show why this matters, let's take the same numbers from the earlier example but assume the institution uses a daily compounding method. This means that the existing balance multiplies every day — including any accrued interest — by the annual interest rate divided by 365. If the annual interest rate is 2%, the daily rate would be 0.00005479.

Because of the more frequent compounding interval, the customer is able to build a slightly higher balance from the same initial balance. Of course, the greater the amount that you deposit, the greater the dollar amount difference will be from compounding. So, while the extra earnings may seem small on a $10,000 opening balance, the difference on, say, a $100,000 account would be significantly greater.

Annual Percentage Yield (APY)

Though it's useful to understand how compounding works, the reality is that you don't necessarily need to perform any complicated math to compare the returns offered by different products. That's because financial institutions will typically publish something called the "annual percentage yield" or APY.

The APY can tell you how much the account will yield based on how often the interest is compounded. So, you don't need to know what interest rate is used to calculate your interest or how often it accrues interest; the APY typically factors all that in.

How Can You Make the Most of Compound Interest?

When trying to save money, compound interest can be significant. Because interest accrues exponentially when it is compounded, the amount credited to one's account can get bigger over time. While the effect may be small in the first year or two, the interest in an account with compound interest would start to "accelerate" after 10, 20 or 30 years.

Therefore, people who save early could reap the biggest benefits of compounding interest. Let's look at another example. Say that a 50-year-old woman opens a savings account that pays a 2% annual rate. If she contributes $100 a month, she'll end up with $13,272 by the time she's 60 years old (assuming interest is compounded monthly and no withdrawals have been made).

But if she had started at age 30, she would have $49,273 in the account by age 60. Because the interest earned in the first few years continues to accrue additional interest, the amount she deposited in her 30s represents a bigger share of her ending balance than the amount she contributed in recent years.

The Bottom Line

When it comes to saving for retirement and managing your finances, understanding compound interest may help you make strategic financial decisions. For more information on how compound interest can impact your retirement savings, consider speaking with a financial representative.

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Information provided is general and educational in nature, and all products or services discussed may not be provided by Western & Southern Financial Group or its member companies (“the Company”). The information is not intended to be, and should not be construed as, legal or tax advice. The Company does not provide legal or tax advice. Laws of a specific state or laws relevant to a particular situation may affect the applicability, accuracy, or completeness of this information. Federal and state laws and regulations are complex and are subject to change. The Company makes no warranties with regard to the information or results obtained by its use. The Company disclaims any liability arising out of your use of, or reliance on, the information. Consult an attorney or tax advisor regarding your specific legal or tax situation.