Compound Interest Calculator

The eighth wonder of the world

Albert Einstein supposedly called compound interest “the eighth wonder of the world” (the quote is apocryphal but the idea is right). Compound interest means your interest earns interest. Year 1, you earn return on your principal. Year 2, you earn return on principal pluslast year's interest. Over decades, this snowballs into exponential growth.

The formula: A = P(1 + r/n)^nt, where A is the final amount, P is the principal, r is the annual rate, n is the number of compoundings per year, and t is time in years. With monthly contributions, the formula adds a series term — but the calculator above handles all of that.

Compound vs simple interest

Simple interest is calculated only on the principal. $10,000 at 7% simple interest earns $700/year, every year. After 30 years: $31,000.

Compound interest at the same rate, compounded annually: $10,000 → $76,123 over 30 years. The difference (~$45,000) is interest earning interest. The longer the time horizon, the more dramatic the gap.

The Rule of 72

A back-of-envelope formula: 72 ÷ annual rate = years to double your money. At 7%: ~10.3 years. At 10%: 7.2 years. At 4%: 18 years. At 12%: 6 years.

The math works because of the natural log of 2 (~0.693), which 72 approximates well for typical interest rates. It lets you do compound projections in your head — useful for sanity-checking financial advisors' claims.

The power of starting early — Sarah vs Julie

A famous illustration. Two friends, both retire at 65, both earn 7% annually:

• Sarah contributes $5,000/year from age 25 to 35 (10 years), then stops. She invested $50,000 total.
• Julie waits until 35 to start, then contributes $5,000/year from 35 to 65 (30 years). She invested $150,000 total.

At 65: Sarah has about $602,000. Julie has about $540,000. Sarah wins despite contributing one-third as much, because her early money had decades longer to compound. Time in the market is more powerful than amount invested.

Realistic return assumptions

What rate should you plug in? Historical averages (US-based, USD-nominal):

• S&P 500 (US large-cap stocks): ~10% nominal, ~7% real (inflation-adjusted) over the past century.
• Total US stock market: ~9–10% nominal historically.
• US bond aggregate: ~4–5% nominal historically; lower in recent decades.
• 60/40 stocks/bonds portfolio: ~7–8% nominal long-term.
• High-yield savings accounts (2026): ~4–5% (rate-sensitive — varies with Fed policy).
• CDs (1-year): ~4–5% currently.

For long-term retirement projections, 7% real return(after inflation) is a common conservative assumption for diversified stock-heavy portfolios. Use inflation-adjusted (“real”) numbers to compare future dollars to today's purchasing power — otherwise $1M in 30 years sounds like a lot but might only have the buying power of ~$400K today (assuming 3% inflation).

Compounding frequency: how often matters less than you'd think

For most retail accounts, compounding frequency is a marketing detail rather than a material factor:

• Annual compounding at 7%: $10,000 → $19,672 in 10 years.
• Monthly compounding at 7%: $10,000 → $20,097 in 10 years.
• Daily compounding at 7%: $10,000 → $20,136 in 10 years.
• Continuous compounding at 7%: $10,000 → $20,138 in 10 years.

The difference between monthly and continuous is tiny. The marketing math (“daily compounding!”) usually doesn't materially change outcomes — focus instead on the rate and the fees.

Tax-advantaged accounts compound faster

In a regular taxable account, you pay capital gains tax on dividends and realized gains, slowing the compounding. Tax-advantaged accounts let your money compound without that drag:

• Roth IRA — contributions taxed up front, withdrawals tax-free. Best when you expect higher taxes in retirement.
• Traditional IRA / 401(k) — contributions deductible now, taxed in retirement. Best when you'll be in a lower bracket later.
• HSA — triple-tax-advantaged for medical expenses. Often the best account if you have access to one.
• 529 plan — tax-free growth for education expenses.

Use our Paycheck Calculator to model how increasing your 401(k) contribution affects take-home pay — the actual cost is less than the contribution amount because of tax savings.

What can derail compound growth

• Fees — 1% in annual fees can eat 25%+ of your final wealth over 40 years. Choose low-cost index funds where possible.
• Behavior — selling at market lows, frequent trading, performance-chasing. Time in the market > timing the market.
• Withdrawing early — pulling money out resets the compounding clock and may trigger taxes/penalties.
• Inflation — high-inflation periods erode real returns. Plan in inflation-adjusted terms.
• Lifestyle creep — failing to increase contributions as income grows.