The Basic Formula: Principal, Rate, and Time

Savings account interest is calculated using your account balance, the annual interest rate the bank offers, and how long your money sits in the account. The simplest version is Interest = Principal × Rate × Time. If you have $1,000 in an account earning 4.5% annually and leave it untouched for one year, you earn $45.

But most banks don't pay interest once a year—they compound it, meaning they calculate interest on your interest. This happens daily, monthly, or quarterly depending on the bank. Compounding is why the real formula is more complex, and why the same rate produces different results at different banks.

The bank's disclosure document, called the Truth in Savings Act disclosure, tells you both the Annual Percentage Rate (APR) and the Annual Percentage Yield (APY). APY is what you actually earn because it includes compounding. Use APY when you calculate what you'll make.

Key Takeaways

  • Simple interest uses the formula Principal × Rate × Time, but most savings accounts compound interest daily or monthly, so you earn interest on your interest.
  • Always use the Annual Percentage Yield (APY) from your bank's disclosure, not the APR, because APY reflects how often interest compounds.
  • The compounding frequency matters: daily compounding earns more than monthly compounding at the same stated rate.
  • You can estimate earnings by multiplying your balance by the APY and dividing by 12 for a monthly estimate, or by 365 for a daily estimate.

How Compounding Changes Your Earnings

When a bank compounds interest, it adds the interest you earned to your balance, then calculates next period's interest on the larger amount. If you start with $1,000 at 4.5% APY compounded daily, the bank divides 4.5% by 365 to get a daily rate of about 0.0123%. On day one, you earn roughly $0.12. On day two, you earn interest on $1,000.12, not just $1,000.

Over a year, this compounding effect adds up. With daily compounding at 4.5% APY, $1,000 grows to $1,046.04—not $1,045. The extra $1.04 comes entirely from compounding. The more often interest compounds, the more you earn. Daily compounding beats monthly compounding, which beats quarterly compounding, all at the same APY.

Your bank's disclosure tells you the compounding frequency. Look for language like "interest compounded daily" or "compounded monthly." If you don't see it, call the bank or check their website—it's required information.

The Compound Interest Formula

If you want to calculate exactly what you'll earn with compounding, use this formula: A = P(1 + r/n)^(nt). Here, A is your final amount, P is your starting balance (principal), r is the APY as a decimal, n is how many times per year interest compounds, and t is the number of years.

Example: $5,000 at 4.5% APY compounded daily for 2 years. Convert 4.5% to 0.045. Daily compounding means n = 365. So: A = 5000(1 + 0.045/365)^(365 × 2). This equals 5000(1.00012329)^730, which gives you $5,472.79. You earned $472.79 in interest.

Most people don't need to do this by hand. Your bank's website usually has a savings calculator, or you can use a free online compound interest calculator. Enter your balance, APY, compounding frequency, and time period, and it does the math. The point of knowing the formula is understanding why the APY on your statement matters more than the interest rate alone.

Monthly and Daily Interest Calculations

If you want a quick estimate without the full formula, you can calculate monthly interest by dividing your APY by 12. A $10,000 balance at 4.5% APY earns roughly $37.50 per month (10,000 × 0.045 ÷ 12). This is approximate because it doesn't account for compounding within the month, but it's close enough for planning.

For a daily estimate, divide the APY by 365. That same $10,000 at 4.5% APY earns about $1.23 per day (10,000 × 0.045 ÷ 365). Again, this is an approximation. The actual daily amount changes slightly as your balance grows from compounding, but the estimate shows you the ballpark.

These quick calculations work best when your balance stays steady. If you're adding money regularly or withdrawing, the actual interest will differ because the bank recalculates based on your current balance each compounding period.

What Happens When Your Balance Changes

Banks calculate interest on your average daily balance or your ending daily balance, depending on their policy. Most use average daily balance, which means they add up what you had each day of the month and divide by the number of days. This matters if you deposit or withdraw mid-month.

If you deposit $5,000 on the 15th of a 30-day month, the bank counts that $5,000 for only 16 days. Your interest for that month is based on a lower average balance than if you'd deposited on the 1st. Conversely, if you withdraw money late in the month, you still earn interest on it for most of the month.

Your bank's disclosure explains which method they use. The difference is usually small—a few cents per month—but it's worth knowing if you're moving money in and out frequently.

Reading Your Bank Statement

Your monthly or quarterly statement shows the interest you actually earned. Look for a line item labeled "Interest Paid" or "Interest Earned." This is the real number—what the bank calculated based on your actual balance and their compounding method. Compare it to your estimate using the APY to see if the bank's calculation makes sense.

If your estimate was $37.50 for the month and the statement shows $35, the difference likely comes from your balance changing during the month or from the compounding method. If the difference is large—say you expected $37 and earned $10—contact the bank. They may have made an error, or the APY may have changed during the period.

Keep statements for at least a year so you can track whether the interest rate stays consistent. Banks can change rates, and you want to know if yours drops significantly.

Frequently Asked Questions

Why does my bank show both APR and APY?

APR is the annual interest rate without compounding. APY includes the effect of compounding, so it's always equal to or higher than the APR. Banks must show both by law, but you should use APY to calculate what you'll actually earn.

Does the interest rate change if I withdraw money?

The rate itself doesn't change, but your interest earnings do because they're based on your balance. If you withdraw $2,000, next month's interest is calculated on the lower balance. Some accounts have tiered rates—higher balances earn higher rates—so a withdrawal might also lower your rate.

How often should I check my interest earnings?

Check your statement each time it arrives—monthly or quarterly—to confirm the interest posted. This catches errors early. You don't need to recalculate every day unless you're tracking growth toward a specific goal.

Can I calculate interest if the rate changes mid-year?

Yes, but you calculate each period separately. If your rate was 4.5% for six months and then dropped to 3.5%, calculate interest for the first six months at 4.5%, then calculate the remaining six months at 3.5%, and add them together. Your statement will show this breakdown.

What's the difference between a savings account and a money market account for interest?

The calculation method is the same—both use APY and compound interest. Money market accounts often offer higher rates but may require a larger minimum balance or limit how many withdrawals you can make per month. The interest math works identically.