Compound interest explorer

Compound interest is the return earned on both your original investment and the interest that has already accumulated. Unlike simple interest — which only pays out on the principal — compound interest pays "interest on interest," so growth accelerates over time. The longer the time horizon, the larger the gap between simple and compound returns. This is why investing earlier matters more than investing larger amounts later.

A little. At 7% APR over 20 years, $10,000 grows to $38,697 compounded annually, $40,135 compounded monthly, and $40,494 compounded daily — roughly a 4.6% gap between annual and daily. Most real investments (stocks, ETFs, bonds) don't compound on a fixed schedule; they fluctuate in market value. The compounding frequency setting here is most useful for modeling savings accounts and CDs, which do quote a specific frequency.

The Rule of 72 says: divide 72 by the annual rate (in percent) to estimate doubling time. So 6% → about 12 years, 9% → about 8 years. It's a mental shortcut, not exact: at 6% the true doubling time is 11.9 years; at 12% it's 6.1 (the rule says 6.0). It's most accurate between 5% and 10%. The footnote under the chart shows the precise figure for your selected rate.

Nominal return is the raw growth of your balance. Real return subtracts inflation. If your investment grows 7% in a year while inflation is 3%, your real return is roughly 4% — that is the actual increase in purchasing power. Over decades the difference compounds: $100,000 over 30 years at 7% nominal becomes ~$761,000 on paper, but only ~$313,000 in today's dollars assuming 3% inflation. Enable the Inflation control under Advanced to see both side by side.

Simple interest pays a flat percentage on the original principal each year. $10,000 at 5% for 30 years earns $15,000 in simple interest, ending at $25,000. Compound interest pays on the growing balance, so the same $10,000 at 5% compounded annually for 30 years grows to about $43,219 — an extra $18,219 from the compounding effect alone. Most investments and savings accounts use compound interest; simple interest is more common for short-term loans and some bond coupons.

Partially. There is an optional "Tax on gains" slider under Advanced that reduces the effective annual return by your specified percentage — useful for modeling a fully-taxable brokerage account. It does not model long-term vs short-term capital gains rates, tax-loss harvesting, or fund expense ratios. Other unmodeled factors: market volatility, sequence-of-returns risk, currency fluctuations. Use this as an order-of-magnitude estimate, not a personal financial plan. For tax-advantaged accounts (Roth IRA, 401(k), ISA), set tax to 0.

The 4% rule is a guideline from the 1998 Trinity Study suggesting that retirees can withdraw 4% of their initial portfolio value each year (adjusted upward for inflation), and have a high probability of not running out of money over a 30-year retirement. So a $1,000,000 portfolio supports roughly $40,000/year. Inverted: divide your annual expenses by 4% to estimate the nest egg you need (e.g. $50k/year ÷ 4% = $1.25M needed). Caveats: the original study assumed a 60/40 stock/bond mix, U.S. historical returns, and a 30-year horizon. For early retirees aiming at 50+ year horizons, more recent research suggests 3.3–3.5% may be safer. The Retire mode in Advanced uses 4% by default but lets you adjust the withdrawal rate.