The two formulas that determine what your bank pays you
Your bank pays you interest in one of two ways: straightforward interest or compound interest. straightforward interest is rare now. Compound interest—where you earn interest on your interest—is what most savings accounts use, and it's what makes your money grow faster over time.
The difference matters. With straightforward interest, $1,000 at 5% annual rate earns $50 per year, every year. With compound interest at the same rate, your earnings accelerate because each month (or day, depending on the account) the bank calculates interest on a larger balance. After one year you'll have earned more than $50.
You don't need to do these calculations yourself—your bank shows the projected earnings in account disclosures and online dashboards. But understanding how they work tells you which account actually pays more and how long it takes to reach a savings goal.
Key Takeaways
- straightforward interest pays a fixed amount each period on your original deposit; compound interest pays interest on your interest, making balances grow faster.
- The Annual Percentage Yield (APY) already includes compounding, so you can compare accounts directly without doing math yourself.
- Compounding frequency matters—daily compounding beats monthly compounding at the same stated rate, because interest accrues more often.
- Your bank must disclose the APY and how often interest compounds in the account agreement or on the product page.
straightforward interest: the straightforward calculation
straightforward interest uses this formula: Interest = Principal × Rate × Time. Principal is your starting balance. Rate is the annual interest rate (as a decimal—so 5% becomes 0.05). Time is how long the money sits there, measured in years.
Example: You deposit $5,000 in an account with a 4% annual straightforward interest rate. After one year, you earn $5,000 × 0.04 × 1 = $200. After two years, you earn another $200 (not $208), because straightforward interest doesn't compound. Your balance is $5,400.
You'll rarely see straightforward interest on savings accounts anymore. It appears on some certificates of deposit (CDs) or older account types, but most banks have moved to compound interest because it's standard in the industry and attracts depositors.
Compound interest: how your earnings accelerate
Compound interest uses this formula: Final Balance = Principal × (1 + Rate/Compounds per year)^(Compounds per year × Years). This looks complex, but the concept is straightforward: the bank adds interest to your balance, then calculates the next interest payment on that larger balance.
Example: You deposit $5,000 at 4% annual rate, compounded daily (365 times per year). After one year, your balance is $5,000 × (1 + 0.04/365)^(365 × 1) = $5,204.04. You earned $204.04, not $200. The extra $4.04 came from earning interest on your interest.
After two years at the same rate, your balance is $5,000 × (1 + 0.04/365)^(365 × 2) = $5,416.65. Notice you earned $212.61 in year two, more than the $200 you earned in year one. That acceleration is compounding at work.
The more frequently interest compounds, the more you earn. Daily compounding beats monthly compounding at the same stated rate. Monthly beats quarterly. Quarterly beats annually. The difference grows larger the longer your money sits in the account.
Why APY is the number that actually matters
Banks state interest rates two ways: the Annual Percentage Rate (APR) and the Annual Percentage Yield (APY). APR is the straightforward rate before compounding. APY is the rate after compounding is factored in—the real return you'll see.
A savings account might advertise 4.00% APR, compounded daily. The APY will be slightly higher—perhaps 4.08%—because that number already includes the effect of daily compounding. When you compare two accounts, always compare APY to APY, not APR to APY. APY tells you what you'll actually earn.
Your bank must disclose both numbers in the account agreement and on the product page. If you see only one, ask which is which before opening the account. The APY is the one that matters for your decision.
How compounding frequency changes your earnings
The same principal and rate produce different results depending on how often the bank compounds. Here's what $10,000 at 5% annual rate earns in one year under different compounding schedules:
| Compounding Frequency | Final Balance After 1 Year | Interest Earned |
|---|---|---|
| Annually | $10,500.00 | $500.00 |
| Quarterly | $10,506.14 | $506.14 |
| Monthly | $10,511.62 | $511.62 |
| Daily | $10,512.67 | $512.67 |
The difference between annual and daily compounding is $12.67 on $10,000 in one year. Over five years at the same rate, daily compounding would earn roughly $70 more than annual compounding on the same deposit. The longer your money stays in the account, the larger the gap grows.
Most online savings accounts compound daily. Traditional brick-and-mortar banks often compound monthly or quarterly. When comparing accounts, check the compounding frequency in the fine print—it's usually listed as "interest is compounded daily" or "monthly" in the account agreement.
Using online calculators and your bank's tools
You don't have to calculate this yourself. Your bank's website usually has a savings calculator where you enter your deposit, the APY, and how long you plan to keep the money. It shows you the projected balance and interest earned.
Many banks also show projected earnings right in your online account dashboard. If you log in and see "Projected earnings this month: $4.23," that's the bank's calculation based on your current balance and the account's APY, accounting for the compounding schedule they use.
If you want to verify the math or compare accounts before opening, use a third-party calculator from a financial education site. Enter the principal, APY, and compounding frequency. The result tells you what you should expect to earn—and whether one account's higher APY is worth switching to.
What happens when interest rates change
Interest rates on savings accounts are not fixed. Banks raise and lower them based on Federal Reserve policy and competition. When your bank changes the rate, the new rate applies to your balance going forward—it doesn't retroactively change what you already earned.
If you opened an account at 5.00% APY and the bank drops it to 4.50% APY next month, you keep the 5.00% rate on the balance you had when the change happened. New deposits or any balance growth from that point forward earns 4.50%. Your bank must notify you of rate changes in writing, usually by email or through your online account.
Because rates change, the APY you see when you open an account is not may provide for the life of the account. If rates fall, your earnings fall with them. If you want to lock in a rate, a CD (certificate of deposit) fixes the rate for a set term—usually three months to five years—but you can't withdraw the money early without a penalty.
Frequently Asked Questions
How often does my bank add interest to my account?
That depends on the account and the bank. Most online savings accounts compound daily but credit interest monthly—meaning the bank calculates interest every day but adds it to your balance once a month. Some credit interest daily. Check your account agreement or ask your bank; the frequency is listed as "interest is credited" or "compounded and credited."
Does the interest I earn get taxed?
Yes. Interest earned on a savings account is taxable income. Your bank sends you a 1099-INT form at the end of the year if you earned $10 or more in interest. You report this on your tax return. The tax rate depends on your overall income and tax bracket, not on the interest rate itself.
What's the difference between APR and APY?
APR is the annual interest rate before compounding. APY is the annual rate after compounding is included. APY is always equal to or higher than APR on a savings account. When comparing accounts, use APY—it shows what you'll actually earn.
Can I calculate interest on money I deposit partway through the year?
Yes, but the calculation changes. If you deposit $5,000 on July 1 in an account with 4% APY, you earn interest only on that $5,000 from July 1 to December 31 (seven months). Use the same formulas, but change "Time" to 0.583 years (7 months ÷ 12 months). Your bank's calculator handles this automatically if you enter the deposit date.
Why do some accounts show higher APY than others?
Online banks typically offer higher APY than traditional banks because they have lower overhead costs. Credit unions sometimes offer competitive rates to members. The APY also depends on the Federal Reserve's current interest rate policy—when the Fed raises rates, banks raise savings rates. When the Fed cuts rates, savings rates fall across the industry.