Required monthly deposit to reach a savings goal

The starting balance is doing work before you contribute anything. It compounds for the whole period, so the deposit only has to cover the gap between what that grows into and the target. A larger opening balance reduces the required deposit by more than its own size.

The required deposit is extremely sensitive to the horizon and only moderately sensitive to the rate. Cutting the time available raises the deposit sharply, because contributions made late have almost no compounding left to help them. Assuming a more optimistic rate helps far less than most people expect, which makes it a poor lever to reach for.

It is possible for the answer to come back at or below zero. That is not an error: it means the existing balance grows past the target on its own and no further deposit is needed. Reading that as a broken result rather than a genuine answer is a common misreading of an inverse calculation.

The target is a nominal amount at the end of the horizon. If it was chosen as an amount that buys something specific, then the number needed will be larger by the time it arrives, and that gap belongs to inflation rather than to this arithmetic.

A forward projection is a flattering instrument. It takes what you are already doing, applies a rate you chose, and reports a number that grows whenever the horizon is stretched — so an uncomfortable plan can always be made to look adequate by pushing the date out. The inverse question refuses that comfort. It fixes the target and the date first, and reports what those two facts demand every month whether or not the demand is affordable.

What the deposits have to fund is narrower than the target, and understanding that is the first useful insight. Whatever is already saved compounds for the full horizon before a single deposit is counted, so the schedule of deposits only has to close the gap between what that opening balance grows into and the target itself. This is why an existing balance reduces the required deposit by more than its own size: it arrives early, and early money is the most heavily compounded money in the arrangement.

The inversion is exact rather than approximate. The pack’s own reference vector for this calculation is a round trip of the forward one — take a projection, hand its ending balance back as a target, and the deposit that comes out is the deposit that went in. That round trip is the cleanest available statement that these are one relation read in two directions, not two calculators that happen to agree.

The required deposit is steeply sensitive to the horizon and only moderately sensitive to the rate, and the asymmetry is structural. Shortening the horizon removes deposits from the schedule and removes compounding from every deposit that remains, and it shortens the run the opening balance gets as well — three losses from one change. Raising the assumed rate helps only the money that is already in the account, and the deposits arriving late are barely helped at all.

This is why halving a horizon raises the required deposit by considerably more than double rather than exactly double, and why the calculator is at its most useful when the horizon is swept rather than fixed. It is also why raising the rate assumption is such a poor way to make an unreachable target look reachable: the input doing the least work is the one being flattered, and unlike the horizon it is not yours to choose. A plan made to work by an optimistic rate has not been changed; only its projection has.

Read the other way, the same asymmetry is encouraging. Extending a deadline is often the cheapest available concession — considerably cheaper per month than any plausible improvement in return — and the calculator prices that concession before it is made. When a target is genuinely fixed to a date, the honest conclusions are the structural ones: a smaller target, more time, or a larger opening balance. Nothing about this page recommends any of them; it prices all three.

An inverse calculation can produce a result at or below nothing, and here it means something precise and welcome: the balance you already hold grows past the target on its own within the horizon, so no further deposit is required to reach it. That is a genuine answer to the question asked, not a malfunction and not a rounding artefact — the schedule of deposits needed to close a gap that has already closed is no schedule at all.

Misreading it is common enough to be worth naming, because a forward-only intuition expects outputs to be positive and reaches for the reload button instead of the interpretation. The useful response is to treat the result as a boundary discovered: the target is comfortably inside reach, and the interesting question has moved on to whether the target was ambitious enough, or whether the horizon could be shortened, or whether the money is committed to the right goal at all.

The figure you enter as a goal is treated as an amount of currency on the end date, not as an amount of buying power. Where the goal is genuinely monetary — repaying a fixed sum, hitting a stated fund level — that is exactly right. Where the goal is really “enough to buy a particular thing”, the amount that buys it will have moved by the time the date arrives, and a plan funded to today’s figure lands short by precisely the erosion in between.

That shortfall is not this calculation’s to include, and building it in silently would be worse than leaving it out: it would bury an assumption about future prices inside an answer about deposits. The honest sequence is to price the erosion separately, restate the target in the money of the end date, and fund that. The inflation page exists for the first step, and it is where this journey goes next.

The remaining assumptions deserve the same daylight. The rate is constant across the whole horizon, deposits are equal and monthly and never missed, and returns sit before inflation, tax and fees. A missed month is not recovered by the arithmetic — it becomes a slightly larger requirement for every month that follows. This is an educational reference, not investment advice.

The engine below is the same one the calculator page runs, verified and mounted mid-lesson. It arrives pre-filled with the pack’s own declared example: a target you would recognise, a modest existing balance, an ordinary rate and a horizon of several years. Read the deposit it demands against what your month could actually carry. Then make two sweeps — halve the horizon and watch the deposit rise by considerably more than double, and raise the rate instead and watch how little it concedes by comparison.

Read the result as the level monthly deposit that lands exactly on the target at the end of the horizon, assuming every deposit is made. A figure at or below nothing means the existing balance gets there unaided. Every figure is computed live by the verified engine from your inputs; this page stores none.