The Basic Formula for Compound Interest

Compound interest is interest earned on both your original deposit and on the interest that has already accumulated. The formula is:

A = P(1 + r/n)^(nt)

Here's what each letter means: A is your final amount, P is your principal (the money you started with), r is the annual interest rate as a decimal (so 2% becomes 0.02), n is how many times per year interest compounds, and t is the number of years. The caret (^) means you raise the number to a power.

Most savings accounts compound daily, which means n = 365. Some compound monthly (n = 12) or quarterly (n = 4). Your bank's disclosure documents will tell you which one applies to your account.

Key Takeaways

  • Compound interest grows faster than simple interest because you earn returns on your accumulated interest, not just your original deposit.
  • The compounding frequency matters: daily compounding produces more growth than monthly or quarterly, though the difference is usually small on typical savings balances.
  • You can calculate compound interest using the formula A = P(1 + r/n)^(nt), or use a calculator or spreadsheet to avoid manual math.
  • The higher your APY and the longer your money stays in the account, the more compound interest you will earn.

Working Through a Real Example

Say you deposit $5,000 in a savings account with an APY of 4.5%, compounding daily, and you leave it untouched for 3 years. Here's how to calculate it:

P = 5,000, r = 0.045, n = 365, t = 3. Plug those into the formula: A = 5,000(1 + 0.045/365)^(365 × 3). That becomes A = 5,000(1 + 0.000123288)^(1,095). Then A = 5,000(1.14308)^, which equals approximately $5,715.40.

Your interest earned is $5,715.40 minus $5,000, or $715.40. That's more than you would earn with simple interest (which would be only $675 over 3 years), because the daily compounding added interest on top of interest.

If the same account compounded monthly instead of daily, the result would be $5,712.93—about $2.50 less. The difference grows smaller as your balance shrinks and larger as your balance grows, but for most people the gap between daily and monthly compounding is modest.

Using a Calculator or Spreadsheet Instead of Doing It by Hand

The formula works, but the math is tedious and error-prone. Most banks provide a compound interest calculator on their website—search "[bank name] compound interest calculator" to find it. These calculators ask you to enter your principal, rate, compounding frequency, and time period, then show you the result instantly.

You can also build a spreadsheet in Excel or Google Sheets. In Google Sheets, the formula would be =P*(1+(r/n))^(n*t), where you replace P, r, n, and t with cell references or numbers. This method lets you change one number (like the interest rate or time period) and see the new total immediately.

A spreadsheet is especially useful if you want to compare scenarios—for example, what happens if you leave the money for 5 years instead of 3, or if rates drop to 3.5%.

Why Compounding Frequency Matters Less Than You Think

Banks advertise daily compounding as a selling point, and it does produce slightly more interest than monthly or quarterly compounding. But the difference is usually small enough that it should not be your main reason to choose one account over another.

On a $5,000 balance at 4.5% for 3 years, daily compounding earns you about $2.50 more than monthly compounding. On a $500 balance, the difference is closer to 25 cents. The APY itself—the rate you're earning—matters far more than how often it compounds.

If you're comparing two savings accounts, focus first on which one offers the higher APY. Then, if the rates are nearly identical, you can use the compounding frequency as a tiebreaker.

How Time and Rate Both Affect Your Growth

The longer your money sits in the account, the more compound interest you earn—but not in a straight line. The growth accelerates over time because you're earning interest on a larger and larger base.

A $5,000 deposit at 4.5% daily compounding earns about $225 in the first year, about $235 in the second year, and about $245 in the third year. Each year you earn more than the last, even though the rate and compounding frequency never change.

The interest rate has an even bigger effect. That same $5,000 at 2% for 3 years grows to about $5,306 (earning $306 total). At 4.5%, it grows to $5,715 (earning $715 total). The difference between a 2% account and a 4.5% account is $409 over 3 years—far larger than any difference between daily and monthly compounding.

What Happens When Interest Rates Change

Most savings accounts today are variable-rate accounts, meaning the bank can change your APY whenever it wants. If rates drop, your new interest earned each day will be smaller. If rates rise, you'll earn more.

The formula still works the same way, but you'll need to recalculate if the rate changes mid-year. If your rate was 4.5% for the first 6 months and then dropped to 3.5% for the next 6 months, you would calculate the interest for each period separately and add them together.

This is why it's worth checking your account's current APY every few months. If rates have dropped significantly and your bank is no longer competitive, you can move your money to a higher-paying account. The interest you've already earned stays with you—you only lose future interest by switching.

Frequently Asked Questions

Does compound interest work the same way for CDs and money market accounts?

Yes. CDs and money market accounts use the same compound interest formula. The main difference is that CDs lock your money in for a set term (3 months, 1 year, 5 years), while savings accounts let you withdraw anytime. Money market accounts often require a higher minimum balance but may offer a higher rate.

What if I make deposits or withdrawals during the year?

The formula assumes your principal stays the same. If you add money or take money out, you'll need to recalculate for each period separately—from the last deposit or withdrawal to the next one. Many banks' calculators have an option to account for regular deposits, which makes this easier.

Is the APY the same as the interest rate?

APY (Annual Percentage Yield) includes the effect of compounding, while the interest rate does not. Banks are required to show you the APY, so use that number in your calculations. It's already built in the compounding effect.

How often does interest actually post to my account?

Most banks compound daily but post interest monthly—meaning they calculate it every day but add it to your balance once a month. Some post quarterly or annually. Check your account agreement or call your bank to confirm. Either way, the daily compounding still happens; posting frequency doesn't change how much you earn.

Can I calculate compound interest on a loan I'm paying off?

Yes, the same formula works for loan interest, but the direction is reversed—the interest is money you owe, not money you earn. Loan interest usually compounds daily as well, which is why paying off a loan early saves you money on interest.