Compound Interest Calculator.

What compound interest actually is

Compound interest is the mechanism by which an account earns interest on interest. Each period, the interest credited to the balance becomes part of the principal for the next period, so the base that earns interest keeps expanding. Simple interest, by contrast, only ever pays on the original principal. Over a single year the difference is small, but over a career it is the difference between a modest sum and a significant one.

The formula

The standard compound interest formula is A = P(1 + r/n)^(nt). Here P is the starting principal, r is the annual rate as a decimal, n is the number of compounding periods per year, t is the number of years, and A is the ending balance. When you add regular contributions, each deposit is future-valued from the day it lands in the account to the end of the term, and all of those individual future values are summed with the future-valued principal.

Example: $10,000 invested at 7% annually for 30 years with no contributions grows to roughly $76,000. Adding $500 per month over the same 30 years lifts the ending balance to roughly $676,000. The contribution stream is nearly nine times more powerful than the starting principal, but the interest is doing the heavy lifting in the final decade.

How compounding frequency affects growth

More frequent compounding produces a slightly higher effective annual yield at the same nominal rate. A 6% rate compounded annually returns exactly 6%; compounded monthly it returns about 6.17%; compounded daily it returns about 6.18%. The jump from annual to monthly is meaningful; the jump from monthly to daily is not. Above roughly monthly compounding, you are chasing basis points rather than percentage points.

The rule of 72

The rule of 72 is a mental-math shortcut for doubling time. Divide 72 by the annual return expressed as a whole number and you get the approximate number of years for the balance to double. A 6% return doubles in about 12 years, an 8% return in about 9 years, a 12% return in about 6 years. The approximation is accurate for rates between roughly 4% and 12%. For very low or very high rates use 69.3 or a direct calculation.

Regular contributions change the shape of the curve

A lump sum grows on an exponential curve; a stream of contributions grows on a shape closer to an accelerating slope. Combined, the two produce the characteristic hockey stick that dominates every realistic savings projection. Contributions dominate for the first third of the horizon, contributions and interest are roughly balanced in the middle third, and interest dominates in the final third. This is why interrupting a contribution stream in the early years costs a small amount but interrupting it in the final years costs relatively little of the ending balance.

Why time is the biggest lever

Two savers, one starting at 25 and one at 35, each contributing the same annual amount at the same return, will not finish anywhere close to each other at retirement. The extra decade of compounding for the earlier saver tends to produce an ending balance roughly twice as large despite only 25% more contributions in total. Rate of return matters, contribution size matters, but time is the only variable that cannot be recovered. The single most valuable action for a young saver is to start.