Compound Interest Calculator
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A compound interest calculator shows how an initial balance grows when interest earned in each period is added to the balance and earns interest in the next period. This recursive growth is what Einstein supposedly called "the eighth wonder of the world." Whether he actually said that is debatable; the math is not.
Enter your starting balance, expected annual rate, time horizon, and how often the account compounds (monthly, daily, etc.). The result shows your final balance and the portion that came from interest rather than your original deposit.
Key takeaway
Compounding's power comes from time, not rate. Doubling your interest rate helps; doubling your time horizon helps far more. A modest 7% rate over 40 years produces roughly the same final balance as a heroic 14% rate over 20 years — and far fewer people earn 14% reliably than have 40 years of investing ahead of them. Start early, then mostly leave it alone.
How it's calculated
The compound interest formula is A = P × (1 + r/n)^(n × t) where:
- A is the final amount
- P is the principal (starting balance)
- r is the annual rate as a decimal (7% → 0.07)
- n is how many times per year interest compounds
- t is the time in years
More frequent compounding produces slightly higher returns, but the
difference between monthly (n = 12) and daily (n = 365) is small —
fractions of a percent over decades. Continuous compounding (the
theoretical limit) gives A = P × e^(rt), just barely higher than daily.
Source: Standard compound interest formula — A = P(1 + r/n)^(nt)
Quick tricks
- Rule of 72 — divide 72 by your interest rate to get years to double. Quick mental math. At 7% return, money doubles every 72/7 ≈ 10 years. At 9%, every 8 years.
- Doubling time × number of doublings = total years. Estimating long-term growth. $10K at 7% over 30 years = three doublings = $80K. (Actual: $76K — pretty close.)
- Compounding frequency matters less than you'd think — daily vs. monthly is fractions of a percent. Comparing accounts. The advertised APY already accounts for compounding frequency, so compare APYs directly.
- Time is more powerful than rate. Choosing between starting early at a low rate vs. starting late at a high rate. The early starter almost always wins.
Examples
$10,000 at 7% over 20 years, monthly compounding
$10,000 invested at 7% with monthly compounding grows to about $40,387 over 20 years. About $30,387 of that — three quarters of the final balance — is interest earned, not original deposit. This is the canonical "let it ride" example.
$10,000 at 7% over 40 years (early start)
Same $10,000, same 7% rate, but doubled to 40 years: $163,098 final balance. Doubling the time horizon roughly quadrupled the result — not doubled. That non-linearity is exactly why starting young matters more than picking the perfect investment.
Frequently asked questions
What's the difference between simple and compound interest?
Simple interest is calculated only on the original principal — $1,000 at 5% earns $50 every year, no matter how long you hold it. Compound interest is calculated on the principal plus all previously earned interest — so the balance grows faster every year. For long time horizons, compound interest produces dramatically larger results. Almost all real-world savings, investment, and loan products use compound interest, not simple.
How does compounding frequency affect returns?
More frequent compounding produces slightly higher final balances, but the effect is small. The same 7% annual rate over 30 years on $10,000 produces about $76,123 with annual compounding, $81,165 with monthly, and $81,629 with daily. The jump from annual to monthly is meaningful; the jump from monthly to daily is rounding. When comparing accounts, focus on the APY (which bakes in the compounding frequency) rather than the APR.
What rate of return is realistic for long-term investing?
Historical US stock market returns average around 10% nominal (7% after inflation) over multi-decade periods. Bond returns have been closer to 5% nominal. A typical balanced portfolio (60% stocks, 40% bonds) has historically returned around 7-8% nominal. Plug in those numbers, but remember historical returns aren't guaranteed and sequence-of-returns risk matters near retirement.
How is this different from APY at a savings account?
Bank savings accounts publish an APY (Annual Percentage Yield) that already accounts for compounding frequency, so you can compare two APYs directly. To use this calculator with a bank's APY, set compounding to 1 per year and enter the APY as the rate — that replicates the bank's published return without double-counting the compounding adjustment.