Compound Interest Calculator

What Is Compound Interest, Really?

Compound interest is the single most powerful mathematical force in personal finance. The basic idea is deceptively simple: instead of earning interest only on the money you originally deposited, you also earn interest on the interest your money has already earned. Repeat that process for decades and the growth curve bends sharply upward — slowly at first, then breathtakingly fast.

To see the difference, imagine you put $10,000 into a savings account earning 7% per year. After year one, you've earned $700 in interest, bringing your balance to $10,700. With simple interest, year two would also earn $700 — because the calculation always applies to the original $10,000. With compound interest, year two earns $749 — because 7% is now calculated on the bigger $10,700 balance. The $49 difference looks like rounding error. But it grows every year. After 30 years, the same $10,000 has become $76,123 under compounding vs only $31,000 under simple interest.

The Formula

For a one-time lump sum invested for t years:

FV = P × (1 + r/n)^{n × t}

Where P is your principal, r is the annual interest rate as a decimal (7% = 0.07), n is the number of compounding periods per year (12 for monthly, 365 for daily), and t is years. When you also make regular contributions, the math adds the future value of an annuity for each contribution. The calculator above runs a month-by-month simulation that handles both cleanly.

The Single Most Important Variable: Time

If there's one lesson from compound interest, it's that time matters more than the amount you save. People intuitively think the size of contributions is what matters. It does, but only somewhat. Time matters far more, because the doubling effect of compounding doesn't kick in fully until 15-20 years into a holding period — and by year 30-40 it's producing growth that no realistic contribution boost can match. A 25-year-old who saves $200/month at 7% finishes wealthier than a 35-year-old saving $400/month at the same return.

The Rule of 72 — Mental Math for Doubling

The Rule of 72 is a handy approximation: 72 ÷ rate = the number of years for money to double. At 6%, your money doubles every 12 years. At 9%, every 8 years. At 12%, every 6 years. The rule is accurate within ~1% for rates between 5% and 15%. It lets you sanity-check any growth claim in your head without a calculator.

Compounding Frequency — A Real but Minor Lever

The more frequently interest compounds, the slightly more you earn. Daily compounding beats monthly, which beats quarterly, which beats annual. At 5% APR, the differences are:

Moving from annual to daily compounding adds about $200 over a decade on a $10,000 balance. Real but minor. APY (Annual Percentage Yield) is the effective annual rate after compounding is applied — that's the number that lets you compare savings accounts apples-to-apples.

Realistic Return Assumptions by Asset Class

Plugging unrealistic return numbers into a compound interest calculator is the easiest way to fool yourself. Long-run historical returns by asset class, in nominal (before-inflation) terms:

For a reasonable long-horizon projection in a diversified stock portfolio, 7% is the standard assumption — it's roughly the inflation-adjusted historical average. Anything above 10% in a 20+ year projection is wishful thinking that ignores both inflation and the historical record.

Tax Drag — The Invisible Compound Killer

This calculator shows nominal pre-tax growth. In a taxable brokerage account, you'll pay capital-gains tax on growth when you sell (15-20% federal in the U.S., plus state). In a Traditional IRA or 401(k), growth compounds tax-deferred but is taxed as ordinary income on withdrawal. In a Roth IRA or HSA, qualified growth is tax-free forever. The order in which you fill these accounts matters enormously over a career — typically: 401(k) up to employer match, then HSA, then Roth IRA, then back to 401(k), then taxable brokerage.

Common Mistakes With Compound Interest

• Assuming 10%+ returns will hold forever. The S&P 500's long-run average is high partly because of one extraordinary U.S. century. Plan for 6-7% real returns; be pleasantly surprised by anything more.
• Ignoring fees. A 1% annual expense ratio compounds destructively. Over 30 years it can consume a third of your gains. Index funds at 0.03-0.10% win by default.
• Stopping contributions during downturns. The math works best when you keep buying through bear markets — that's when you pick up shares cheaply. Stopping at the bottom is the most expensive instinct in investing.
• Conflating nominal and real returns. "I made 10%" sounds great until you remember inflation was 4% that year — your real return was 6%.
• Withdrawing during accumulation. Each withdrawal pulls future compounded gains with it. The dollar you withdraw at 30 would have been many dollars at 65.

Frequently Asked Questions