Compound Interest

Compound interest is return earned on returns already earned. The distinction from simple interest is the entire point: simple interest pays only on the original principal, while compound interest pays on principal plus everything accumulated so far, so the balance curve bends upward rather than running straight.

With regular contributions the calculation has two parts. The lump sum grows as FV = P(1+r)^n. The contribution stream grows as PMT x [((1+r)^n - 1) / r]. The calculator sums them. Over short horizons the contributions dominate and the total looks roughly linear. Over long horizons growth dominates, and in a multi-decade projection the majority of the final balance is typically return rather than the money you put in.

Time is the input the maths rewards most, because n sits in an exponent while the others do not. A useful shortcut is the Rule of 72: divide 72 by the annual percentage return to approximate the years needed to double. At 8% that is roughly nine years; at 4%, roughly eighteen. Doubling the rate more than doubles the outcome over a long horizon, and starting a decade earlier can matter more than contributing more.

Two honest caveats. Projections assume a constant return, but real markets deliver an uneven sequence, and the order of good and bad years matters once you are withdrawing rather than accumulating. And the rate you should enter is the real return — nominal return minus inflation — if you want the answer in today's purchasing power. Entering a nominal return gives a future-dollar figure that overstates what it will buy. Everything runs in your browser — no login, no upload, and no figure you enter leaves the page.