How this instrument works
This instrument answers a specific question: saving toward a fixed dollar figure by a set date, with some money already set aside, how much has to go in every month between now and then? It runs in two steps. First, Current savings toward the goal, $ is projected forward on its own, using Assumed annual return, % compounded once a month for the full span in Months until the goal date — that produces Current savings, grown to the goal date. Whatever gap remains between that grown figure and Goal amount, $ is the only amount new deposits actually have to close.
The second step is the future-value-of-an-annuity formula, solved backwards. Ordinarily that formula takes a level monthly payment and reports the balance it grows into; here the balance is fixed — the remaining gap — and the payment is unknown, so the same growth factor, (1+g)ⁿ minus one over g, moves to the other side of the equation. Each monthly deposit earns interest only from the day it lands, so a deposit made in the final month contributes its face value and nothing more, while one made in month one has almost the whole span left to compound.
People running this arithmetic are usually saving toward something with a real deadline attached — a wedding date already booked, a lease that ends, a trip with tickets to buy — rather than an open-ended objective like retirement, which is why the instrument asks for a month count instead of a target age. It assumes the return holds steady and every deposit lands on schedule; taxes on interest, account fees, and a rate that drifts between now and the deadline are left for the saver to account for separately.
- Enter the target dollar figure into Goal amount, $ — what you want in hand by the deadline.
- Enter what's already set aside into Current savings toward the goal, $.
- Set Months until the goal date to the number of months between now and when the money is needed.
- Set Assumed annual return, % to what the savings will earn while they sit; use 0 for plain cash.
- Read Current savings, grown to the goal date for what the existing balance becomes on its own.
- Read Required monthly contribution for the level deposit needed each month to close the rest of the gap.
Worked example — a $20,000 goal in 24 months
Set Goal amount, $ to 20000, Current savings toward the goal, $ to 2000, Months until the goal date to 24, and Assumed annual return, % to 4. The monthly rate that 4% a year implies is g = 4 ⁄ 1200 = 0.003333, so Current savings, grown to the goal date reads $2,166.29 — the $2,000 already set aside, left untouched and earning that rate for 24 months, with no extra dollar added.
The remaining gap is $20,000 minus $2,166.29, or $17,833.71, and spreading that across 24 monthly deposits at the same rate — each one earning interest only from the day it lands — gives a Required monthly contribution of $714.98. Growth on the existing $2,000 supplies $166.29 of the goal by itself; the new monthly deposits, plus whatever they individually earn along the way, cover everything else.
Questions
Why does the instrument grow my current savings separately from my monthly contribution?
Because the two pots have different histories. Money already in Current savings toward the goal, $ has the entire span in Months until the goal date to compound, so it is projected forward on its own first. What's left over — that target minus the grown balance — is the only amount monthly deposits have to cover, and each deposit earns interest for a different stretch depending on when it lands.
What happens if I set Assumed annual return, % to zero?
The required-contribution formula collapses to plain division: with g at zero, (goal − FV0) divided by ((1+g)ⁿ − 1) becomes (goal − currentSavings) divided by monthsToGoal, since growth stops contributing anything. That is the same math a jar of cash under a mattress implies — nothing earned on savings already made, and nothing expected from future deposits either.
Why is the required monthly contribution less than a simple (goal minus savings) divided by months?
Because that simpler calculation ignores compounding twice over — it neither grows the current savings before subtracting them nor credits monthly deposits with any interest they will earn while they sit. On the default sheet, ($20,000 − $2,000) ⁄ 24 comes to $750.00 flat, while this instrument answers $714.98; the difference is what growth contributes on both sides of the equation.
Does this assume my monthly deposit lands on a fixed schedule?
Yes — an ordinary annuity, meaning every deposit is treated as landing at the end of its month and earning interest from that point on, with none skipped or made early. A deposit that actually lands at the start of a month, or a payment missed once and doubled the next, finishes slightly ahead of or behind this figure; the instrument reports what a level, on-time schedule requires.
Can I use this for a target that isn't a wedding or a house?
Yes — the arithmetic does not know or care what the money is for. Any dollar figure with a deadline and a starting balance works: a trip, a car, a business cash reserve, a holiday fund reset every year. What changes from case to case is the return honestly expected while the money waits, which should reflect where it is actually parked, not a hoped-for market average.
What does this figure leave out?
Taxes on any interest or gains the savings earn, account fees, and any change in rate between now and the deadline. It also assumes Assumed annual return, % holds steady for the entire span in Months until the goal date, which a savings account might deliver but a market-linked account rarely does over a short horizon. Read the output as what a steady, guaranteed rate would require, not a promise that the target gets reached.
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.