Savings goal solver

$1,789.94 a month, from a $0 start, over 30 years, at 7% nominal / 4.39% real, with contributions landing at month end: $455,634 contributed and $544,366 from returns. That figure is in today's purchasing power; the same plan needs $2,097,568 in the actual future dollars $1,000,000 will be worth 30 years from now, because inflation is real here rather than assumed away.

Most savings calculators only run forward: pick a contribution, see what it grows to, and adjust by trial and error until the number matches the goal. This inverts the identity directly, so the answer above is solved rather than guessed at.

The return-solve mode above answers a different question than the contribution solve: not "how much do I need to save", but "is what I'm already planning to save even enough, at a return I could defend". Take $2,000 a month for 10 years toward $1,000,000 from a standing start: that plan requires 28.65% a year, after inflation, every year, for the full decade.

That is not an investing problem a better fund solves. It is the goal, the horizon, or the contribution that has to move; our position is that a tool should say that rather than print the number neutrally and let the reader go shopping for a strategy that promises it.

Four of the five inversions of the savings identity have closed forms and are solved directly. The required return does not, so it is bracketed by bisection between -99% and 1000% and polished by Newton steps that are only accepted when they reduce the residual. That bracket reaches below zero deliberately: when contributions alone overshoot the goal, the required return is negative, and a solver that starts at zero would simply report failure.

None of this models volatility: a single constant return, applied every month, is a deliberate simplification, which is why the answer is a plan rather than a forecast. The balance actually landed on depends on the order the returns arrive in, which the sequence of returns calculator is built to show.