The formula and what each number means
Compound interest grows your savings faster than straightforward interest because you earn interest on the interest itself. The formula is:
A = P(1 + r/n)^(nt)
Here is what each letter represents: A is your final balance. P is the amount you start with (principal). r is the annual interest rate as a decimal (so 4.5% becomes 0.045). n is how many times per year the bank compounds interest. t is the number of years you leave the money untouched.
Most savings accounts compound daily, which means n = 365. Some compound monthly (n = 12) or quarterly (n = 4). Your account statement or the bank's disclosure document will tell you which one applies to you.
Key Takeaways
- The compound interest formula is A = P(1 + r/n)^(nt), where P is what you deposit, r is the annual rate as a decimal, n is how often interest compounds per year, and t is years.
- Daily compounding (n = 365) earns slightly more than monthly or quarterly because interest gets calculated and added more often.
- You can calculate by hand using the formula, or use a spreadsheet or online calculator to avoid arithmetic mistakes.
- The longer you leave money untouched and the higher the rate, the more compound interest works in your favor.
A concrete example with real numbers
Say you deposit $5,000 in a savings account that pays 4.5% annual interest, compounded daily. You plan to leave it for 3 years. Here is how to work through the formula:
P = 5,000 (your deposit) r = 0.045 (4.5% as a decimal) n = 365 (daily compounding) t = 3 (years)
Plug these into the formula: A = 5,000(1 + 0.045/365)^(365 × 3)
First, divide the rate by the compounding periods: 0.045 ÷ 365 = 0.000123288
Add 1: 1 + 0.000123288 = 1.000123288
Multiply the exponent: 365 × 3 = 1,095
Raise to the power: 1.000123288^1,095 = 1.14314
Multiply by principal: 5,000 × 1.14314 = $5,715.70
Your final balance after 3 years is $5,715.70. The compound interest earned is $715.70. If the account had paid straightforward interest instead (interest only on the original $5,000), you would have earned only $675, so compounding added $40.70 to your account.
Why daily compounding matters more than you might think
The difference between daily and monthly compounding looks small on paper, but it adds up over time. Using the same example above, if the account compounded monthly instead of daily, your final balance would be $5,714.08 instead of $5,715.70. That is a $1.62 difference on a $5,000 deposit over 3 years.
The reason is timing. With daily compounding, interest gets added to your account 365 times per year. With monthly compounding, it gets added only 12 times. Each time interest is added, the next calculation includes that new amount, so more frequent compounding means more interest earning interest.
This effect grows larger the longer your money sits in the account and the higher the interest rate. Over 10 years at 5% annual interest, daily compounding could earn you $50 to $100 more than monthly compounding on a $10,000 deposit, depending on the exact terms.
Using a spreadsheet instead of calculating by hand
Most people do not calculate compound interest by hand. A spreadsheet is faster and removes the risk of arithmetic errors. In Excel or Google Sheets, you can use the formula =P*(1+r/n)^(n*t) directly, or you can use the built-in function =FV().
The FV function works like this: =FV(rate, nper, pmt, pv). rate is the interest rate per compounding period (annual rate divided by n). nper is the total number of compounding periods (n times t). pmt is any regular deposit you make (leave this blank if you are not adding money). pv is your starting balance as a negative number (so -5000, not 5000).
For the example above, you would enter: =FV(0.045/365, 365*3, 0, -5000). The spreadsheet returns 5715.70, matching the hand calculation.
If you add money regularly—say $100 per month—you can include that in the pmt field. The spreadsheet will calculate how much interest you earn on both your original deposit and all the deposits you add along the way.
How the interest rate affects your final balance
The annual percentage yield (APY) your bank advertises already includes the effect of compounding, so you do not need to adjust it. However, understanding how sensitive your balance is to rate changes helps you decide whether switching banks is worth the effort.
Using the same $5,000 deposit over 3 years, here is what different rates produce:
| Annual Rate | Final Balance | Interest Earned |
|---|---|---|
| 2.0% | $5,306.04 | $306.04 |
| 3.5% | $5,540.27 | $540.27 |
| 4.5% | $5,715.70 | $715.70 |
| 5.5% | $5,896.36 | $896.36 |
A 1% difference in rate does not sound like much, but it adds up to roughly $180 more in interest over 3 years on a $5,000 deposit. On larger deposits or longer time periods, the gap widens. This is why comparing rates across banks before you deposit matters.
What happens when you add money regularly
Most people do not deposit a lump sum and leave it alone. If you add money monthly, the calculation becomes more complex because each deposit starts earning interest from the moment it hits your account.
A spreadsheet handles this automatically if you use the FV function with a monthly deposit amount. If you want to calculate by hand, you treat each deposit as its own compound interest problem, then add the results together. A $100 deposit made 12 months into your savings period earns interest for only 2 years, not 3, so it grows less than your initial deposit.
For most people, using a spreadsheet or an online savings calculator is the practical choice. You enter your starting balance, monthly deposit amount, annual rate, and time period, and the tool does the math.
The difference between APY and the stated interest rate
Banks are required to show you the APY (annual percentage yield) on savings accounts. The APY already includes the effect of compounding, so it is higher than the stated interest rate. If a bank says the interest rate is 4.5% compounded daily, the APY might be 4.60%.
When you see the APY advertised, you can use that number directly in your calculations without worrying about the compounding frequency. The APY is the actual return you will see on your money over one year. For longer periods, use the stated interest rate and compounding frequency with the formula above, because the APY applies only to a one-year period.
Frequently Asked Questions
Do I need to know the formula if I can use a calculator?
No. Understanding what the numbers mean is more useful than memorizing the formula. A spreadsheet or online calculator will do the math correctly. What matters is knowing what rate to use, how often it compounds, and how long your money will sit in the account.
What if my bank does not tell me how often interest compounds?
Call the bank or check your account agreement. Most savings accounts compound daily, but some older accounts or specialty products compound monthly or quarterly. The compounding frequency is always disclosed in writing because it affects your return.
Does compound interest work the same way for CDs and money market accounts?
Yes. The formula is identical. The main difference is that CDs lock your money for a set period (3 months, 1 year, 5 years), and money market accounts may have withdrawal limits. The compounding mechanics are the same.
If I withdraw money early, do I lose all the interest?
Not all of it, but you may lose some. Most savings accounts let you withdraw without penalty. CDs charge an early withdrawal penalty that reduces your interest earnings. Check your account terms to see what applies to you.
Why does the bank show me a different balance than my calculation?
Banks round differently, use slightly different day counts, or may have fees that reduce your balance. Small differences (a few cents) are normal. Large differences mean you should ask the bank to explain the calculation.