How compound interest works

Simple interest is earned only on your principal. Compound interest is earned on your principal plus all the interest you have already accumulated. That distinction sounds small but produces enormous differences over time — each period's interest becomes part of the base that earns next period's interest.

The standard compound interest formula is: A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate, n is the number of compounding periods per year, and t is time in years. Our calculator extends this to include recurring contributions, which is how most real-world investing actually works.

Why compounding frequency matters less than you think

All else equal, more frequent compounding produces a higher return — daily compounding beats annual compounding. But the difference between monthly and daily compounding is tiny. The frequency that matters far more is how often you contribute.

• Annual vs. monthly compounding on $10,000 at 7% for 20 years: the difference is about $200.
• Contributing $500/month vs. $6,000/year (same total) at 7% for 20 years: the monthly approach yields roughly $20,000 more because contributions start compounding sooner.

The lesson: focus on contribution size and consistency over compounding frequency.

The Rule of 72

The Rule of 72 is a quick mental shortcut: divide 72 by your annual return rate to estimate how many years it takes to double your money.

• At 6%: 72 ÷ 6 = 12 years to double
• At 8%: 72 ÷ 8 = 9 years to double
• At 10%: 72 ÷ 10 = 7.2 years to double

This is approximate but accurate enough for planning. It also works in reverse — if you want to double your money in 10 years, you need a roughly 7.2% annual return.

What return rate should you use?

The right rate depends on what you are investing in. Common reference points:

• S&P 500 index funds: historically around 10% nominal (7% after inflation) per year over long periods, though with significant year-to-year variance.
• Diversified stock/bond portfolios: typically 5–8% depending on the mix.
• High-yield savings / CDs: 4–5% in today's rate environment.
• Treasury bonds: 4–5% at current yields.

For long-horizon retirement projections, many planners use 6–7% as a conservative real-return assumption for a diversified equity portfolio. Using an optimistic rate inflates your projected balance — when in doubt, model with a lower number and treat the upside as a bonus.

The impact of starting early

Time is the most powerful variable in compound growth — more powerful than the return rate or contribution size. A common illustration:

• Investor A starts at 25, contributes $300/month until 65 (40 years). At 7%, ending balance: ~$793,000.
• Investor B starts at 35, contributes $600/month until 65 (30 years) — twice as much per month. At 7%, ending balance: ~$680,000.

Starting 10 years later and doubling the contribution still produces a lower final balance. The decade of early compounding is irreplaceable. This is why time in the market consistently outperforms timing the market.

Tax-advantaged accounts: 401(k), IRA, Roth IRA

The calculator models pre-tax growth. In taxable accounts, dividends and capital gains are taxed annually, which meaningfully reduces effective compounding. Tax-advantaged accounts remove this drag:

• Traditional 401(k) / IRA: contributions are pre-tax (reduce taxable income now); withdrawals in retirement are taxed as ordinary income.
• Roth IRA / Roth 401(k): contributions are after-tax; qualified withdrawals (including all growth) are completely tax-free.

For most people, maximizing tax-advantaged space before investing in taxable accounts is the highest-leverage move available. The 2025 contribution limits are $7,000/year for IRAs ($8,000 if 50+) and $23,500 for 401(k)s ($31,000 if 50+).

Inflation and real returns

A 7% nominal return does not mean your purchasing power grows 7% per year. Inflation — historically around 2–3% annually in the US — erodes the real value of your balance. The real return is approximately: nominal rate − inflation rate.

At 7% nominal with 3% inflation, your real return is roughly 4%. This means a $1,000,000 balance in 30 years has roughly the purchasing power of $400,000–$500,000 today. For retirement planning, always consider whether your projections beat inflation, not just whether the nominal number looks large.