Required monthly deposit to reach a savings goal

What a target actually demands each month

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.

When this calculation is used

• Turning a fixed target — a deposit, a fund, a purchase at a known date — into a monthly figure you can commit to.
• Testing whether a target is reachable at all within the time available before committing to it.
• Seeing how much the required deposit falls if the horizon is extended rather than the rate assumption raised.
• Checking what an existing balance is already contributing towards a goal.

Worked example

Take a target you would recognise — a deposit or a fund — with a modest existing balance, an ordinary rate and a horizon of several years.

The single output is the level monthly deposit that lands exactly on the target at the end of the horizon, given that the existing balance is compounding alongside it. It assumes you make every deposit; a missed month is not recovered by the arithmetic.

Halve the horizon and read the deposit again. It rises by considerably more than double, because you lose both the deposits you would have made and all the compounding those and the starting balance would have earned. Time is the input worth protecting.

What each input represents

Assumptions and limits

• The rate is constant for the whole horizon.
• Deposits are equal, monthly, and made at the end of each period without exception.
• The annual rate is divided into monthly periods — a nominal convention rather than an effective annual rate.
• The goal is a nominal amount at the end date, not an inflation-adjusted one.
• Returns are before inflation, tax and fees.

What the guards protect against

• The horizon must be greater than zero — a goal due immediately cannot be funded by a schedule of deposits.
• The rate is bounded to a realistic range; outside it the result would not describe any account and is refused rather than answered.
• A goal below zero is refused. A negative target is not a saving problem.

Provenance

Standard ordinary-annuity relation, solved for the payment

The future-value target net of the compounded starting principal, divided by the future-value annuity factor for the monthly periods in the horizon.

Educational reference, not investment advice. The signed pack carries its own citation; the page reports the verification state of the release it mounted rather than asserting one.