The three questions a savings goal really asks
A dated savings goal has three unknowns and you only ever get to fix two of them: the amount, the monthly deposit, and the time. Fix the amount and the date, and the deposit follows. Fix the amount and the deposit, and the date follows. Fix the deposit and the date, and you find out what you can actually afford to want. This calculator solves all three at once so you can see the trade rather than guessing at it.
The starting balance matters more than people expect, because it works for the whole horizon rather than being dripped in. A $5,000 balance at 4% APY becomes $5,849.29 over four years without you doing anything, and every dollar of that is a dollar the monthly deposit does not have to supply. That is why the calculator subtracts the future value of what you already hold from the goal, not its present value.
Everything here assumes a savings-style account whose balance does not fall. That assumption is safe for cash and unsafe for investments, which matters most for exactly the goals people are tempted to invest — a house deposit two years out is the classic case where a bad quarter arrives at the worst moment.
Where the formula comes from
Money deposited at the end of each month for n months is an ordinary annuity. The first deposit earns interest for n − 1 months, the second for n − 2, and the last for none, so the total at the end is PMT × ((1 + r)n − 1) / r. That fraction is the annuity factor, and it is simply the sum of the geometric series of growth factors written in closed form.
Your existing balance is a separate, simpler term: it compounds for the full n months, so it becomes P(1 + r)n. Put the two together and the balance at the end is P(1 + r)n + PMT × ((1 + r)n − 1) / r. Setting that equal to your goal F and rearranging for PMT gives the formula above — the required deposit is the part of the goal your existing savings will not supply, divided by the annuity factor.
Solving for time instead needs a logarithm, because n sits in an exponent. Rearranged, n = ln((F·r + PMT) / (P·r + PMT)) / ln(1 + r). Two things fall out of that expression. It has no solution when P·r + PMT is zero or negative — no deposit and no interest means no progress — and it grows without bound as the deposit shrinks towards the level that only services the gap, which is the savings mirror image of a loan payment that only covers the interest.
The monthly rate is derived as (1 + APY)1/12 − 1, not APY ÷ 12. An APY already includes its own compounding, so dividing by twelve applies it twice. At 4% APY the correct monthly rate is 0.327374% against 0.333333% for the naive version, and the difference compounds in your favour on the page and against you in reality.
Worked example: $25,000 in four years with $5,000 already saved
You want $25,000 for a house deposit in four years. You have $5,000 saved and the account pays 4.00% APY.
- Monthly rate. (1.04)1/12 − 1 = 0.00327374.
- Months. 4 × 12 = 48.
- Growth factor. 1.0032737448 = 1.1698586, which is just 1.044 written monthly.
- What today's savings become. 5,000 × 1.1698586 = $5,849.29.
- What the deposits must supply. 25,000 − 5,849.29 = $19,150.71.
- Annuity factor. (1.1698586 − 1) ÷ 0.00327374 = 51.8852.
- Required deposit. 19,150.71 ÷ 51.8852 = $369.10 a month.
Check it the other way: 369.10 × 51.8852 = $19,150.7 of deposits and growth, plus the $5,849.29 the opening balance became, is $25,000.0. If instead you deposit the $400 the calculator loads with, the balance at 48 months is 5,849.29 + 400 × 51.8852 = $26,603.36, so you clear the goal with $1,603.36 to spare — and you would reach $25,000 itself during month 45, three months early.
Reading the result when the number is uncomfortable
The required monthly deposit is the honest answer, and it is often larger than the amount you had in mind. There are only four levers and it is worth knowing their relative strength.
Time is the strongest. The required deposit is roughly inversely proportional to the horizon: doubling the years roughly halves the monthly amount, and slightly more than halves it once interest is included. Pushing a goal from three years to five cuts the deposit by about 40%.
The goal itself is next. It scales exactly: a goal 20% smaller needs a deposit 20% smaller, holding everything else constant. Trimming the target is unglamorous and immediate.
Existing savings help in proportion to their future value, so moving $1,000 into the goal removes $1,000 × (1 + r)n from what the deposits must supply — at 4% over four years, $1,169.94 of work for $1,000 of money.
The rate is the weakest lever over short horizons, and this surprises people. On the worked example above, dropping the APY from 4% to 0% raises the required deposit from $369.10 to (25,000 − 5,000) ÷ 48 = $416.67, a difference of $47.57 a month. Worth having, but not the thing that decides whether the goal is reachable. Over twenty years the ranking reverses and the rate dominates — which is exactly why cash is the right home for a four-year goal and the wrong one for a retirement goal.
Monthly deposit needed per $10,000 of goal
| Horizon | 0% APY | 2% APY | 4% APY | 5% APY |
|---|---|---|---|---|
| 1 year | $833.33 | $825.79 | $818.43 | $814.82 |
| 2 years | $416.67 | $408.81 | $401.19 | $397.48 |
| 3 years | $277.78 | $269.83 | $262.18 | $258.47 |
| 5 years | $166.67 | $158.68 | $151.11 | $147.46 |
| 7 years | $119.05 | $111.08 | $103.62 | $100.08 |
| 10 years | $83.33 | $75.42 | $68.17 | $64.78 |
Read the ten-year row against the one-year row: interest supplies a growing share of the goal as the horizon lengthens, and almost none of it inside a year.
Assumptions worth checking before you trust the date
- The deposit arrives every month without fail. A plan built on the best month of the year fails in an ordinary one. Use a figure that survives a month with a car repair in it.
- The APY holds for the whole horizon. Savings rates are variable. For a multi-year goal, run the calculation again at a rate two points lower and see whether the plan still works.
- The goal is in today's dollars. For anything more than a couple of years out, the thing you are buying gets more expensive too. Age the target with the inflation purchasing power calculator before you commit to a number.
- Deposits land at month end. Depositing at the start of each month multiplies the annuity portion by (1 + r) and reaches the goal marginally sooner.
- Nothing is withdrawn. If this account doubles as your emergency reserve, one genuine emergency resets the plan. Keep the two separate and size the reserve with the emergency fund calculator.
- Tax is ignored. Interest in a taxable account is ordinary income, so the effective yield is roughly APY × (1 − your marginal rate). Enter the after-tax yield if you want the conservative version.
Choosing where the money sits
Match the account to the horizon. Under a year, an on-demand high-yield savings account is almost always right, and the savings account interest calculator will compare the offers you are looking at. One to five years, a certificate of deposit or a Treasury of matching maturity usually pays more, and the penalty for breaking it is the price of the certainty you are buying. Beyond five years and for goals with no fixed date, the interest-bearing account model on this page understates what a diversified portfolio has historically returned, but it also understates the risk, and neither is captured by an APY field.
Two goals deserve their own treatment. Education saving has a dedicated tax-advantaged wrapper, so run the numbers through the 529 college savings calculator rather than this one. And a house deposit interacts with what you can borrow: the deposit target itself should come out of the home affordability calculator, because the amount you need is set by the price you can support, not the other way round.