Savings Goal Planner

A savings target contains four quantities — the goal, what you have, how long you have, and the return you expect. Fix any three and the fourth is determined. This planner lets you choose which one to solve for, so the same target can be approached from whichever direction matches the question you are actually asking.

Solving for the contribution answers "how much should I save each month?" Solving for time answers "when will I get there at my current rate?" Solving for the balance answers "is this plan enough?" All three read the same period-by-period schedule; only the unknown changes, so the three answers are always consistent with one another.

The schedule itself is the source of truth rather than a formula applied afterwards. That matters once a plan is anything other than level: contributions can rise each year, they can land at the start or the end of each period, and the last contribution before the goal is trimmed to the amount actually needed instead of overshooting. A closed form cannot describe any of those, so the calculator does not use one to produce the answer — only to check it.

The growth share is the most useful diagnostic here. On a short goal it will be small — the five-year example below is about 11% growth and 89% saving — which is reassuring, because it means the plan does not depend on markets cooperating. Stretch the same goal to ten years and growth carries roughly a fifth of it, and the return assumption starts to matter.

Match the expected return to the account you will actually use. A three-year goal held in cash earns cash rates; entering an equity return produces a deposit that is too small and a plan that can fail at exactly the wrong moment. This is the most common way a savings plan is set up to disappoint.

When the required contribution is uncomfortable, extend the deadline before raising the assumed return. The sensitivity matrix makes the comparison direct: in the worked example, moving from five years to seven cuts the required deposit by about a third, while moving the return from 4% to 6% cuts it by about 7%. Time is the lever that reduces the deposit without adding risk; the return assumption reduces it by adding risk.

In time-to-goal mode, read the final contribution alongside the duration. If it is much smaller than the scheduled amount, you cross the goal early in that period and the plan effectively arrives a fraction of a period sooner than the whole-period count suggests.

One schedule produces every result on this page. The balance is advanced one contribution period at a time, and each of the three modes is a different question asked of that same schedule: mode 1 searches for the contribution that ends on the target, mode 2 reports the period at which the balance first reaches it, and mode 3 simply runs it and reports where it lands.

The entered return is an effective annual rate, matching the rest of the site. The period rate is i = (1 + r)^(1/n) − 1 for n contributions a year, so switching from monthly to weekly saving changes the number of deposits without secretly changing the return earned. A 4% annual return is 4% a year at every frequency offered.

Contribution timing changes the order of operations inside each period, and nothing else. At end-of-period the balance earns growth first and the contribution is added afterwards, so the first deposit earns nothing in its own period. At start-of-period the contribution is added first and then the whole balance grows, so every deposit earns one extra period of return. In the worked example this is the difference between $608.45 and $606.47 a month.

An annual contribution increase raises the deposit once per year, on the anniversary — every period inside year one uses the base amount, every period inside year two uses base × (1 + g), and so on. The increase applies to the scheduled deposit, so mode 1 solves for the year-one amount and the later years follow from it.

Solving for the contribution uses bisection over that schedule rather than algebra, because the schedule is what the answer has to satisfy. The ending balance rises monotonically with the contribution, which is what makes bisection valid: the upper bound starts at the target divided by the number of periods and is doubled until it clears the target (at most 40 doublings), the bracket is then narrowed until it is under a twentieth of a cent or 200 iterations have run, and the solved figure is fed back through the full schedule so the residual against the target is reported rather than assumed. When the plan is level and end-of-period the ordinary annuity closed form is computed alongside it and both are shown, so a disagreement would be visible rather than silent.

Solving for time has no clean closed form once there is an existing balance, escalation or start-of-period timing, so the schedule is advanced until the closing balance first reaches the target. That period is the answer, counted in whole contribution periods. If the target has not been reached within 100 years the goal is reported as unreachable under those assumptions instead of the search continuing.

Because the goal is usually crossed part-way through a period, the last contribution is reduced to the amount that lands exactly on the target — the partial final contribution. Earlier contributions are never altered. At end-of-period timing that amount is target − balance after growth; at start-of-period it is target ÷ (1 + i) − balance, because the trimmed deposit will itself earn one period of return. This is why the ending balance in time mode is the target exactly and the overshoot is zero.

The solved contribution is verified in the test suite from three independent directions: an annuity closed form written separately from the engine, a reference schedule loop written separately from the engine, and the site's own future value calculator run forward on the solved figure. All three have to agree on the target to within a rounding tolerance.

This calculator solves for an unknown against a fixed target. If you already know the deposit and only want the ending balance, with escalation and timing options but no goal to hit, the future value of regular payments calculator is the direct tool for that; this one adds the reverse solves and the goal-crossing behaviour on top of the same arithmetic.

Target $50,000 in five years, starting from $8,000, at a 4% effective annual return, saving monthly at the end of each period. The monthly rate is (1.04)^(1/12) − 1 = 0.0032737, and there are 60 contributions. The solver returns $608.45 a month; the closed form returns $608.45 as well, so the two agree to the cent. Running that deposit back through the schedule ends at $49,999.85 — fifteen cents short, because the deposit itself is rounded to the cent.

Over the five years that is $36,507 of deposits and $5,492.85 of growth, which is about 11% of the ending balance. On a five-year horizon saving does the work and returns are a modest contributor. Moving the same deposits to the start of each month would cut the required saving to $606.47, a difference of $1.98 a month — small, but free.

Asked the other way round, a fixed $600 a month reaches $50,000 after 61 months — five years and one month. The 61st contribution is not $600 but $397.51, because that is all that is needed to land exactly on $50,000 rather than overshoot it. Asked the third way, that same $600 a month over exactly five years reaches $49,440.64, leaving a $559.36 gap: the plan is 98.9% of the way there, which is what the extra month is buying.

Stretching the goal date changes the picture far more than the return does. At ten years the required deposit falls to $260.12 a month — a 57% reduction — because the deposits have twice as long to compound and there are twice as many of them, and growth's share of the ending balance rises from 11% to about 22%.