What Is the Daily Compound Interest Formula?

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DEFINITION

Daily compounding interest is the daily interest earned on your savings account balance after interest from the previous day is added.

Daily compounding interest is the interest you earn on your savings account added back to your account balance. Banks use it as an incentive for you to keep money in savings.

Learn more about daily compounding interest, how to calculate it, and how much your money can earn in a savings account.

Definition and Examples of Daily Compounding Interest

Daily compounding interest is a financial incentive banks use as payment for using your money and as an incentive to keep it in a savings account. The basic idea is that you earn interest on the original sum of money you deposited, called the principal. That interest is added to your principal, 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, say you have an account that gives you 1% annually compounding daily. You start with $100, so you'd earn .00274% daily (1% ÷ 365) in interest, and you end up with $100.0000274. The next day, you'll earn another .00274%. At the end of one year (365 days), you'd have $101.01.

How Do You Calculate Daily Compounding Interest?

To calculate compound interest, use the following formula:

Compound Interest Formula

Where:

  • A = the total future value. or what you'll have
  • P = the initial deposit
  • r = the interest rate
  • n = the number of times that interest is compounded per period
  • t = the number of periods

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.

Here's how the calculation would look for a $100 deposit without additional deposits after one year: $100 ( 1 + ( 1% ÷ 365 ) )365x1 = $101.01.

Most online calculators and Excel will yield different results because of differences in programming. Calculating daily compounding interest manually with the formula can also yield different results than the automated methods.

Compounding Daily Interest With Regular Deposits

If you want to calculate how much you'd have in your savings account after a year of regular deposits the formula is:

If you started with $100 in your savings account that offers 1% annual interest compounded daily and made $100 deposits once a month for a year, you'd add the deposit to the last balance and run the calculation again:

  • $100 + $101.01 ( 1 + ( 1% ÷ 365 ) )365 = $203.03
  • $100 + $203.03 ( 1 + ( 1% ÷ 365 ) )365 = $306.07
  • $100 + $306.07 ( 1 + ( 1% ÷ 365 ) )365 = $410.15
  • $100 + $410.15 ( 1 + ( 1% ÷ 365 ) )365 = $511.16

After one year, you'd end up with around $1,308, $1,300 of which were your deposits—so you'd earn about $8 over 12 months.

How Compounding Interest Works

Compounding interest makes your money grow following this sequence:

  • The principal in an account earns interest over a predetermined period.
  • The interest is added to the principal.
  • The new total earns interest.
  • The new interest is added to the balance.
  • 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.

How To Calculate Daily Compound Interest in Excel

Excel and Google Sheets use the future value function to calculate compound interest. You'll need all the information used in the previous examples for the function to work.

The function formula is:

Excel Future Value Function

Where:

  • Rate = Interest rate per period
  • Nper = Number of periods
  • Pmt = Payment made per period. A negative number is used.
  • Pv = Present value; the lump sum amount that a series of payments is worth. A negative number is used. Optional.
  • Type = Payments due at the end of period (0) or beginning of period (1). Optional.
Excel Daily Compounding

Limitations of Daily Compounding

Daily compounding interest, while an excellent way to use your money to make money, is limited in scope when used in a savings account because you'll rarely find one that pays enough interest to make an impact. In the above examples, you earned about $180 by continuously adding $100 to your account every month for one year. If you had only let the account compound on the initial amount of $100, you'd have made a little more than $1.

How much difference did daily compounding make? It would barely outpace inflation—which at a rate of 5% per year would take more purchasing power away than money you're earning. For instance, if your $100 turned into $101.01, but inflation was 5% the following year, that $101.01 could only purchase $95.95 worth of goods or services. The Federal Reserve's target inflation rate is 2% per year—most savings accounts do not offer rates close to this, so your money is losing value by staying in a savings account.

Savings accounts are suitable for storing money, but they are not designed to increase your wealth.

You could put $250,000 into a savings account (the maximum protected by the FDIC). Many "high-yield" saving accounts offer rates around 1.05%. At this rate, you will end up with about $13,500 extra in your pocket after five years. However, most people will not be able to afford this, so a $1,000 principal with $100 monthly deposits is more realistic. This would give you about $210 in interest over a five-year period.

As a consumer and saver, you should understand that daily compounding does matter, but your savings account isn't going to make you rich. Savings accounts are suitable for saving money—but compounding interest works better on products with higher interest rates using more funds.

Key Takeaways

  • Compounding interest uses interest on interest to make money grow.
  • The more you place into an account that compounds interest, the more you can earn.
  • Savings account daily compounding interest rates are not high enough to keep up with inflation.
  • Savings accounts are best used to store emergency funds or other funds you intend to use for something else but are not suitable for building wealth.

Article Sources

  1. Board of Governors of the Federal Reserve System. "Why Does the Federal Reserve Aim for Inflation of 2 Percent Over the Longer Run?"

  2. Federal Deposit Insurance Corporation. "Are My Deposit Accounts Insured by the FDIC?"