Compound Interest Calculator
Compound interest is the reason small, steady savings can turn into large sums, and the reason small debts can spiral if left unpaid. This calculator shows you exactly how it works on your numbers. Enter your starting amount, interest rate, compounding frequency, and time period to see your final balance, total interest earned, and a year-by-year breakdown of how the growth builds.
What Compound Interest Actually Means
Compound interest is interest paid on interest. Put $1,000 in an account earning 5% a year, and after year one you have $1,050. In year two, that 5% applies to $1,050, not the original $1,000 — so you earn $52.50, not $50. That extra $2.50 looks small on its own, but it's the entire idea: every year, the base the interest is calculated on gets a little bigger, so the dollar amount of interest keeps rising even though the rate never changes. Left alone for long enough, this turns into the single biggest driver of long-term growth in savings and investing.
The Compound Interest Formula
A = P(1 + r/n)nt
Here, A is the final amount, P is the principal (starting amount), r is the annual interest rate written as a decimal (6% becomes 0.06), n is how many times per year interest compounds, and t is the number of years. To find just the interest earned, subtract the principal from the final amount: Interest = A − P. The calculator above runs this same formula, plus adds in any regular contributions you specify, so you get both the math and a clear picture of how it builds year by year.
Simple Interest vs. Compound Interest
| Simple Interest | Compound Interest | |
|---|---|---|
| Calculated on | Original principal only | Principal plus all previously earned interest |
| Growth pattern | Straight line (linear) | Curves upward (exponential) |
| $1,000 at 5% after 20 years | $2,000 | $2,653 (annual compounding) |
| Common use | Some short-term loans | Savings accounts, investments, most loans and credit cards |
The gap between the two grows wider the longer the money sits. Over a handful of years it's a modest difference; over multiple decades, compound interest can produce a dramatically larger balance than simple interest ever would from the same starting rate.
Why Compounding Frequency Matters
The n in the formula — how often interest compounds — changes the outcome even when the stated annual rate stays identical. Daily compounding adds interest to the balance 365 times a year; annual compounding adds it just once. Since each addition starts earning its own interest sooner under daily compounding, the final balance ends up slightly higher than the same rate compounded annually. The difference is usually modest for typical savings rates, but it grows with higher interest rates and longer time periods. Use the compounding frequency selector above to see the exact difference on your own numbers.
The Rule of 72
The Rule of 72 is a shortcut for estimating how long it takes money to double: divide 72 by the annual interest rate. At 6%, money doubles in about 12 years (72 ÷ 6). At 9%, it doubles in about 8 years. It's not exact — the real answer depends on compounding frequency too — but it's close enough to be genuinely useful for a quick mental estimate without opening a calculator at all.
| Annual Rate | Years to Double (Rule of 72) |
|---|---|
| 3% | ~24 years |
| 6% | ~12 years |
| 9% | ~8 years |
| 12% | ~6 years |
APY vs. APR
APR (Annual Percentage Rate) is the stated yearly rate, without factoring in how often it compounds. APY (Annual Percentage Yield) is the actual return you get once compounding is factored in — which is why APY is always equal to or higher than APR for the same account. A savings account advertising "5% APY" with monthly compounding actually has a slightly lower APR behind it, since the APY already includes the extra growth from compounding. When comparing accounts, APY is the more accurate number to look at, because it reflects what you'll actually earn.
Adding Regular Contributions
Most real-world savings don't sit untouched — people add to them regularly. The "Monthly Contribution" field above layers recurring deposits on top of the base compound interest formula, which is closer to how a typical savings account or investment account actually behaves. Even a modest recurring contribution can meaningfully change the final balance, because every dollar added earlier has more time to compound than a dollar added later. This is the same principle behind an investment calculator, just isolated here to focus specifically on the interest mechanics.
Compound Interest Works Against You Too
Everything above applies just as much to debt as it does to savings. Credit card balances typically compound daily or monthly — unpaid interest gets added to the balance, and then that larger balance starts accruing interest of its own. This is exactly why a credit card balance can grow faster than expected if only minimum payments are made: the "interest on interest" effect that builds wealth in a savings account is the same effect that builds debt when a balance isn't paid down. An amortization calculator shows the mirror-image process for a fixed-rate loan being paid off on schedule.
Getting the Most Out of Compounding
- Start as early as possible. Time in the market matters more than almost any other factor, since compounding needs years to really show its effect.
- Leave the interest alone. Withdrawing earned interest resets the base back to the original principal and stops the "interest on interest" effect.
- Add to the balance regularly. Even small, consistent contributions compound alongside the original principal.
- Compare APY, not just the stated rate, when choosing between savings accounts or CDs.
- Pay down high-interest debt aggressively. Compounding on a credit card balance works against you exactly as effectively as it works for you in a savings account.
Frequently Asked Questions
Q: What is compound interest?
A: Compound interest is interest calculated on both the original principal and on interest already earned, so a balance grows faster over time than it would with simple interest, which is calculated only on the original principal.
Q: What is the compound interest formula?
A: The compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times interest compounds per year, and t is the number of years.
Q: How does compounding frequency affect growth?
A: More frequent compounding, such as daily or monthly instead of annually, produces a slightly higher final balance at the same stated annual rate, because interest is added to the balance more often and starts earning its own interest sooner.
Q: What is the Rule of 72?
A: The Rule of 72 is a quick way to estimate how many years it takes for money to double at a given annual interest rate: divide 72 by the interest rate. At 6% interest, for example, money doubles in roughly 12 years.
Q: What is the difference between APY and APR?
A: APR (Annual Percentage Rate) is the stated interest rate without accounting for compounding within the year, while APY (Annual Percentage Yield) reflects the actual return including the effect of compounding, so APY is always equal to or higher than APR for the same account.
Q: Does compound interest apply to debt as well as savings?
A: Yes. Compound interest works the same way on debt, such as credit card balances, meaning unpaid interest gets added to the balance and then itself starts accruing interest, which is why carrying a balance can grow faster than many people expect.
This calculator provides estimates for informational purposes only and does not constitute financial advice. Actual rates, compounding terms, and returns vary by account and are not guaranteed. Consult a licensed financial professional for guidance specific to your situation.