How this instrument works
Most savings arithmetic runs forward: pick a monthly deposit, watch it compound, see what pile it becomes. This instrument runs the other direction. A parent needs $50,000 set aside for a move in five years and already has $5,000 earning 4% — the question is not what that $5,000 will grow into on its own, but what monthly deposit, added on top and compounding alongside it, closes the remaining gap by the deadline. That reversal is the entire point of a goal-seeking savings tool: the target and the date are fixed inputs, and the deposit is the unknown being solved for.
The shape of the formula follows from one accounting identity: by the deadline, the current balance will have grown on its own to PV(1+r)^N, and the stream of monthly deposits will have compounded into its own separate lump sum. Add those two pieces together and the sum must equal the goal. Rearranging that equality for the deposit is what produces the formula below — it is nothing more than future-value arithmetic solved backward, subtracting what the existing balance already contributes before dividing the remainder across the compounding power of the deposits still to come.
The number only holds if every input holds too: the rate stays constant for the whole stretch, every deposit lands on schedule without a missed month, and the balance is untouched until the deadline. Markets do not deliver a flat return, and a single skipped month means the following ones must run larger to recover — treat the figure as the steady, frictionless deposit a plan would need under those conditions, then build in a margin above it.
- Enter the dollar figure you are aiming for into Savings goal, $.
- Enter what is already set aside toward it into Current savings balance, $ — enter 0 if starting from nothing.
- Set Annual interest rate, % to the return the balance is expected to earn; the field will not accept zero.
- Set Time to reach the goal, years to the number of years until the deadline.
- Read Required monthly contribution, $ — the flat amount to deposit every month from now until the deadline.
Worked example — $50,000 in five years from a $5,000 start
Set Savings goal, $ to 50000, Current savings balance, $ to 5000, Annual interest rate, % to 4, and Time to reach the goal, years to 5. The monthly rate is r = 4 ÷ 1200 = 0.003333, and N = 5 × 12 = 60 deposits stand between now and the deadline. Left alone, the $5,000 already on hand grows to roughly $6,105 by the deadline — a real contribution toward the goal, but nowhere near enough on its own. Required monthly contribution, $ reads $662.08, the flat deposit that closes the remaining distance.
Widen the horizon to eight years instead of five and the required deposit drops well below $400, because a longer stretch both adds more deposits and gives each one more months to compound. Shorten it to two years and the figure climbs past $1,800 — the same $45,000 gap divided across far fewer compounding periods demands a much larger monthly share. The deposit is far more sensitive to the deadline than to small moves in the rate, which is the habit this instrument is built to correct.
Questions
Why does this ask for a deposit instead of a future balance?
Because the balance and the date are usually fixed by something outside the plan — a tuition bill, a lease deadline, a wedding booked a year out — and the deposit is the only figure left to choose. A calculator that instead asks for a deposit and reports what it grows into answers a different question: what a chosen habit produces, not what a fixed target requires.
Why is the existing balance not just subtracted from the goal?
Because the balance you already hold keeps earning its own return while the deposits run. Simple subtraction — (goal minus current balance) divided by months — ignores that growth entirely and overstates the monthly amount needed, sometimes by a wide margin over a long horizon. The formula credits the starting balance with its own compounding first, then sizes the deposit against what remains.
Why did the required deposit fall so much when the timeline moved from five years to eight?
Two effects stack in the same direction: more months means the gap is split into more pieces, and each deposit also gets more time to compound before the deadline arrives. Both effects shrink the required amount, which is why lengthening the horizon by a few years often does more for the monthly figure than chasing a higher rate.
What if the current balance is already projected to exceed the goal?
The formula returns a negative figure, which reads as money that could be withdrawn each month while still reaching the goal — not a deposit obligation. In practice a fast-approaching goal that is already funded is worth revisiting with a lower-risk rate assumption rather than treating the negative number as spendable.
Why does the field reject a zero interest rate?
The formula divides by (1+r)^N minus 1, which collapses to zero when r is zero, making the expression undefined. At an effectively zero rate the arithmetic is simpler anyway and does not need this formula: Required monthly contribution, $ is just the remaining gap divided evenly across the months, since nothing is compounding.
What does this figure leave out?
It assumes one constant rate for the entire stretch, a deposit made without exception every month, and no taxes, fees, or account minimums taken out along the way. A savings or brokerage account rarely holds a flat rate for years at a stretch, so treat the output as the steady deposit a frictionless plan would require, then add a buffer above it rather than aiming at the figure exactly.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.