What Is the Daily Compound Interest Formula?

How to Calculate Daily Compound Interest

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Compounding interest is interest on an initial amount of money added to the original amount. Interest is then earned on that amount, and so on. It is one of the fundamental concepts for using your money to build wealth.

Definition and Examples of Compounding Interest

Compound interest is a powerful tool used by many people and businesses to achieve their financial goals. The basic idea is that you earn interest on the original sum of money you deposited. That interest is added to your account, and you then earn interest on the new amount. The new interest you earn will be more than the previous amount, and it grows larger every time you receive an interest payment.

For example, if you start with $100 and earn 1% annually in interest, you end up with $101. The next time interest is calculated, you will earn 1% of $101, giving you a total of $102.01. The next time, you'll earn interest on that amount. The amount continues to grow as it earns interest.

How Do You Calculate Daily Compounding Interest?

To calculate compound interest, use the following formula:

Compound Interest Formula

Here is how the formula breaks down:

  • A = the total future value
  • P = the initial deposit
  • r = the interest rate
  • n = the number of times that interest is compounded per period
  • t = the number of periods that have passed

You can also multiply the amount by the interest rate and add the interest to it, then multiply that amount by the interest rate. Continue doing this until you've reached the number of periods you're trying to figure for (the formula is much faster).

Over time, compound interest can create additional income, provided you have enough principal generating interest. The more you can deposit, the more you’ll earn long-term as your deposits and interest accumulate.

How Compounding Interest Works

Compounding interest follows the following sequence to make your money grow:

  • The principal in an account earns interest over a predetermined period.
  • The interest is placed into the account and adds to the principal.
  • The new total earns interest.
  • The new interest is added to the account.
  • The new amount earns interest, and the cycle continues.

The formula simplifies this sequence and gives you an estimate of how much money you'll end up with over the time frame you calculated. The formula works for daily, monthly, annual, or any other compounding periods you might come across.

Daily vs. Monthly Compounding

Assume you’ve opened an online savings account and deposited $10,000. Your goal is to leave that money alone for five full years and let it grow. And let’s also assume that this bank pays an interest rate of 2%, with interest compounding every month. How much money will you have five years from now?

To determine the first interest payment, you begin with $10,000 and multiply it by 0.02. That comes to $200. Next, you divide $200 by 12 to determine the monthly interest to be credited ($200/12 = $16.67). Then add the $16.67 to your original principal of $10,000 to get $10,016.67. The following month you would multiply that figure by 0.02, divide it by 12, and add it to the principal balance. You would repeat the process each month. Over the course of five years, you’ll get 60 interest payments.

Using a compound interest formula (or an online compound interest calculator), you can determine that you’ll generate $1,050.79 overall, totaling $11,050.79 at the end of five years. But what if a bank claims it will compound interest daily? In this case, you make the same calculations 365 times per year instead of 12. The calculation shows that you’ll earn $1,051.68 over the course of five years, giving you a total of $11,051.68.

How much difference did daily compounding make? Your additional savings came to $0.89 in five years. Obviously, this isn't a significant amount. In fact, it would barely outpace inflation.

Inflation can steal your interest gains very quickly. For example, if you'd placed your money in an account in 2016 and let it grow for five years, by 2021, you'd only have gained about $9 of purchasing power even with the $1,051.68 gain.

Even if you put $250,000 into a savings account (the maximum protected by the FDIC), you will end up with about $20 extra in your pocket after five years. Perhaps you could buy yourself lunch, but not much else.

Daily compounding of interest from your savings account might net you a few cents, but not much more. If your bank offers you daily compound interest, you shouldn't turn it down. However, remember that daily compounding makes only a minimal difference in how much you can ultimately save.

As a consumer and saver, you should understand that daily compounding matters far less than the interest rate being paid and any fees you may incur. So don’t overlook other bank account features in favor of daily compounding interest.

Key Takeaways

  • Compounding interest uses interest on interest to make money grow.
  • There is a minimal difference between daily and monthly compounding.
  • The more you place into an account that compounds interest, the more you will earn.