The Basic Formula for Compound Interest
Compound interest grows your money by earning interest on the interest you've already accumulated. The formula is: A = P(1 + r/n)^(nt), where A is your final amount, P is what you started with, r is the annual interest rate as a decimal, n is how many times interest compounds per year, and t is the number of years.
Most savings accounts compound daily or monthly. Daily compounding means your bank calculates and adds interest to your account 365 times a year. Monthly compounding does it 12 times. The more often interest compounds, the more you earn, because each time the bank adds interest, the next calculation includes that new amount.
To use the formula, convert your APY to a decimal by dividing by 100. If your account earns 4.5% APY, that becomes 0.045. Then plug in the numbers and solve. A calculator or spreadsheet makes this faster than doing it by hand.
Key Takeaways
- The compound interest formula A = P(1 + r/n)^(nt) calculates your total balance after interest has been added multiple times over your holding period.
- Daily compounding (n=365) earns slightly more than monthly (n=12) because interest is calculated and added to your balance more often.
- You can calculate compound interest using a spreadsheet, online calculator, or the formula by hand if you convert your APY to decimal form first.
- The difference between simple and compound interest grows larger over time and with higher balances, which is why long-term savings benefit most from compounding.
Working Through a Real Example
Say you deposit $5,000 in a savings account earning 4.5% APY, compounded daily, and leave it untouched for 3 years. Here's how to calculate it:
P = $5,000, r = 0.045, n = 365, t = 3. Plug these into the formula: A = 5000(1 + 0.045/365)^(365 × 3). First, divide 0.045 by 365 to get 0.000123288. Add 1 to get 1.000123288. Raise that to the power of 1095 (365 times 3). The result is approximately 1.1432. Multiply by $5,000 to get $5,716.
Your $5,000 earned about $716 in interest over three years. If the account had used simple interest instead (interest calculated only on the original $5,000), you would have earned only $675. Compound interest added $41 to your return in this example.
Why Compounding Frequency Matters
The difference between daily and monthly compounding is small on a $5,000 balance over a few years, but it grows with larger amounts and longer time periods. On $50,000 over 10 years at 4.5% APY, daily compounding earns roughly $50 to $100 more than monthly compounding, depending on the exact dates.
Some banks advertise "continuous compounding," which uses a different formula (A = Pe^(rt)) and theoretically compounds infinitely. In practice, the difference between continuous and daily compounding is negligible for consumer savings accounts—usually less than a dollar per year on typical balances.
When comparing savings accounts, the APY already accounts for compounding frequency. A bank that compounds daily will show a higher APY than one compounding monthly, even if both have the same stated interest rate. Always compare APY, not the base rate, to see which account actually pays more.
Using a Spreadsheet to Calculate Compound Interest
Most people find a spreadsheet easier than the formula. In Excel, Google Sheets, or similar programs, you can set up columns for your starting balance, interest rate, compounding frequency, and time period, then use a formula to calculate the result.
In Excel, the formula would be: =P*(1+(r/n))^(n*t), where you replace P, r, n, and t with cell references or numbers. For example, if your starting balance is in cell A1, your APY in B1, compounding frequency in C1, and years in D1, you'd write: =A1*(1+(B1/C1))^(C1*D1). Press Enter and the spreadsheet calculates your final balance instantly.
You can also create a month-by-month or year-by-year breakdown by calculating the balance after each compounding period. This shows you exactly when your interest accelerates and helps you see the real impact of leaving money untouched.
The Difference Between Compound and Simple Interest
Simple interest is calculated only on your original deposit. If you put $10,000 in an account earning 5% simple interest, you earn $500 per year, every year, for a total of $5,000 over 10 years. Your final balance is $15,000.
Compound interest is calculated on your original deposit plus all accumulated interest. The same $10,000 at 5% compounded annually grows to about $16,289 after 10 years—$1,289 more than simple interest. The longer your money sits, the bigger this gap becomes, because you're earning interest on increasingly larger amounts.
All savings accounts use compound interest, not simple interest. Loans sometimes use simple interest, but that's a different calculation. For savings, compounding is always in your favor.
What Happens When You Make Deposits or Withdrawals
The formula above assumes you deposit money once and never touch it. Real savings accounts usually involve deposits and withdrawals. Each time you add money, the next compounding period includes that new amount. Each time you withdraw, the balance shrinks.
To calculate interest on an account with multiple deposits, you can either use the formula for each deposit separately (treating each as its own starting balance for the time it sits in the account) or use a month-by-month spreadsheet that adds deposits and subtracts withdrawals, then recalculates the balance after each compounding period.
Many banks show your interest earned in your account statement, so you don't have to calculate it yourself. But knowing how to do it helps you compare accounts and understand whether you're getting a fair return on your money.
Online Calculators and Bank Tools
Most banks provide a compound interest calculator on their website, usually near the savings account product page. You enter your starting balance, APY, and time period, and it shows your final balance and total interest earned. These calculators use the same formula but save you the math.
Free calculators are also available from financial websites and educational resources. They often let you adjust compounding frequency, add regular deposits, and see results year by year. Some even show how inflation affects your purchasing power, which is useful for long-term planning.
If you're comparing multiple accounts, using the same calculator for each one ensures you're using consistent assumptions. This makes it easier to see which account actually pays the most over your time horizon.
Frequently Asked Questions
Does compound interest work the same way for all savings accounts?
Yes, the formula is the same, but the APY varies by bank and account type. High-yield savings accounts compound the same way as regular savings accounts—the difference is the interest rate itself. A high-yield account at 4.5% APY will always outpace a regular account at 0.5% APY, regardless of compounding frequency.
What's the difference between APY and the interest rate?
The interest rate is the base percentage your bank pays. APY is the annual percentage yield, which includes the effect of compounding. APY is always equal to or higher than the interest rate. When comparing accounts, always use APY, because it shows the true return you'll receive.
How often should I check my compound interest calculations?
You don't need to calculate it yourself regularly—your bank does this automatically and shows your balance in your account. But calculating it once when you open an account helps you understand what to expect. Recalculate if you change banks or if interest rates change significantly.
Can I lose money from compound interest?
No. Compound interest only adds to your balance. You earn interest on interest, which accelerates growth. The only way your balance shrinks is if you withdraw money or if fees exceed your interest earnings, which is rare in savings accounts.
Why does my bank's calculation differ slightly from mine?
Banks may round differently, use slightly different day counts (365 vs. 360 days), or apply interest on different dates than you assumed. These differences are usually a few cents to a few dollars per year on typical balances and don't affect your overall return meaningfully.