Compound Interest Calculator

Simple interest applies the rate only to the original principal: $10,000 at 7% earns $700 every year, forever. After 30 years you've earned $21,000. Compound interest applies the rate to the running balance, which means each year's interest joins the principal and itself starts earning interest. The same $10,000 at 7%, compounded annually, becomes $76,123 after 30 years — more than 3.6× the simple-interest result.

The shape of the growth curve is the key intuition. For the first decade or two, simple and compound returns look similar; the gap then opens up sharply. Most of the dollars in a 30-year compounded account are earned in the last 10 years, which is why "start early" is the most important investing advice and why mid-career savers cannot easily compensate with a higher rate.

The same nominal annual rate compounds to a different effective rate depending on how often the interest is added. 6% compounded annually returns 6% per year; 6% compounded monthly returns about 6.17%; daily, about 6.18%. Continuous compounding (the theoretical limit) returns about 6.184%. The differences are small but real — over 30 years on $100,000, the gap between annual and daily compounding is roughly $5,000.

Be wary of confusing nominal rate with annual percentage yield (APY). When comparing savings accounts or CDs, always compare APY to APY: it normalizes for compounding frequency and is the actual return you'll receive.

A common mistake is to chase a slightly higher return by taking on substantially more risk, when extending the time horizon would have produced more growth with less worry. $10,000 at 7% over 40 years grows to $149,745. $10,000 at 9% over 30 years grows to $132,677. The lower-return, longer-horizon investment wins by about $17,000 — without any of the volatility cost of the higher-return strategy.

This is one reason starting retirement contributions in your twenties is so disproportionately valuable. The first $5,000 contributed at age 25 will, at a 7% real return, be worth roughly $76,000 by age 65. The same $5,000 contributed at 45 grows to about $19,000 in those same years. Same dollars, four times the result, just from time.

Divide 72 by your annual return to estimate the years needed to double your money. At 7%: ~10.3 years. At 9%: ~8 years. At 4%: 18 years. At 12%: 6 years. The rule is an approximation — derived from the natural logarithm — that's accurate to within a few percent for rates between 4% and 15%, which covers most realistic investment scenarios.

The same shortcut works in reverse: at 3% inflation, prices double in roughly 24 years. Combining the two: an investment earning 7% real (after-inflation) doubles real purchasing power every 10 years; nominally it doubles closer to every 7 years at 10% gross.