Compound interest is what happens when the interest a balance earns is left in place and starts earning interest in turn. The mechanism is unremarkable in any single period and dramatic across many: the return in each period is applied to a base that is larger than the one before, so growth is multiplicative rather than additive, and the resulting curve bends upward continuously.
The practical consequence is that time, not rate, is the dominant variable over long horizons. Doubling a rate doubles the annual accrual; extending a horizon by a decade changes the shape of the whole outcome. This page models a single lump sum with no further contributions, which is the cleanest case for seeing that effect without the arithmetic of monthly deposits getting in the way.
With P the principal, rate the nominal annual rate as a percentage, n the number of compounding periods per year and t the term in years:
final = P × (1 + rate ÷ 100 ÷ n) ^ (n × t)
interest = final − P
growth per cent = interest ÷ P × 100
The frequency selector offers yearly (1), quarterly (4), monthly (12) and daily (365). If the nominal rate is zero, final equals the principal and the growth row has no denominator to divide by, so it displays a dash. Note also that the growth figure is a total percentage over the whole term, not an annual one — do not read it as a yearly return.
The fourth row is the one to compare products with. The effective annual yield is what a year of compounding actually produces:
APY = ((1 + rate ÷ 100 ÷ n) ^ n − 1) × 100
10,000 at 6 per cent for 10 years, compounded monthly:
Changing only the frequency shows how little the daily option buys at this rate and term: yearly gives 17,908.48, quarterly 18,140.18, monthly 18,193.97 and daily 18,220.29. Daily compounding beats yearly by 311.81 over ten years — real money, but 26.32 of that is the step from monthly to daily, which almost never justifies choosing a product on frequency alone. The effective yields, 6.00, 6.14, 6.17 and 6.18 per cent, tell the same story in a form that is comparable across any compounding convention.
For a rough check on doubling, divide 72 by the annual rate: at 6 per cent that suggests twelve years, and the exact answer is 11.9 years. The rule is a rule of thumb, and it drifts at high rates, but it is accurate enough to sanity-check a projection.
Because compounding inside the year adds to the return. A 6 per cent nominal rate compounded monthly delivers 6.17 per cent over a full year. The APY is the honest number when comparing products, since it already accounts for frequency.
Marginally. In the default case it adds 26.32 over ten years, about 0.14 per cent of the final balance. Treat a daily-compounding offer as essentially equivalent to monthly and compare the underlying rates instead.
Not directly. This page assumes the principal is left untouched. Adding money each month changes the future value materially, and the SIP page in this suite applies the correct annuity formula.
Anything entered here is an assumption, not a forecast. Broad equity markets have historically returned more than cash over long periods and have also suffered decades of flat or negative real returns. Running the same figures at a low, middle and high rate is more informative than trusting any single one.
Only in whether interest is reinvested. Simple interest multiplies the principal by the rate and the time once and stops; this page applies the rate repeatedly to a growing balance. At a 5 per cent rate over three years the difference is 76.25 on 10,000 — small. Over thirty years it decides the outcome.