Savings goal calculator

How the formula works

This calculator runs the compound-interest machinery in reverse. Instead of asking what a deposit grows to, it fixes the ending balance — the goal \(G\) — and solves for the monthly deposit \(C\) that lands exactly there. Two things grow toward the goal: what you have already saved, \(P\), and the stream of end-of-month deposits. Setting their combined future value equal to the goal:

and solving for \(C\):

where \(n\) is the number of monthly deposits and \(i\) the monthly rate. Savings accounts quote an APY, which is an annual effective yield — compounding is already baked in — so the matching monthly rate is not APY ÷ 12 but the rate that compounds up to the APY over twelve months:

At 4% APY that is 0.327% a month rather than the 0.333% that APY ÷ 12 would give — a small distinction that keeps the arithmetic honest. Two edge cases the formula handles: at a 0% rate the equation collapses to the plain split \(C = (G-P)/n\), and if \(P\,(1+i)^n\) already exceeds the goal, the required deposit is zero — the head start gets there on its own.

Notice where \(i\) appears: inside \((1+i)^n\). Over a short horizon \(n\) is small, the growth factor stays close to 1, and the rate barely moves the answer — saving is almost pure division. Over a long horizon the exponent compounds the rate into a large factor and the APY starts doing real work. The questions below put numbers on both.

What each input means

Goal amount — \(G\)

The balance you want on the day you need the money: the car, the roof, the tuition bill, the emergency fund target. It is a future-dollar figure — see the assumptions below on inflation.

Time to reach it — \(t\)

Years until you need the money; decimals work, so 18 months is 1.5. The calculator converts it to \(n = 12t\) monthly deposits (rounded to whole months).

Already saved — \(P\)

What is set aside for this goal today. It compounds untouched for the whole period, so every dollar here shrinks the required deposit by more than a dollar spread over the months.

Account APY — \(r\)

The advertised annual percentage yield on wherever the money sits. APY already includes compounding, which is why the monthly rate is derived with the formula above rather than divided by 12. Real APYs float with the market; enter today's and revisit when it changes.

A worked example

The worksheet's defaults: a $20,000 goal in 3 years, $2,000 already saved, at 4% APY.

• Monthly rate: \(i = 1.04^{1/12} - 1 = 0.003274\) — not \(0.04/12 = 0.003333\), because APY is an effective yield.
• Over \(n = 36\) months the growth factor is \((1+i)^{36} = 1.124864\) — exactly \(1.04^3\), as an effective rate should give.
• The head start grows on its own: $2,000 × 1.124864 = $2,249.73, leaving $20,000 − $2,249.73 = $17,750.27 for the deposits to cover.
• Each monthly dollar accumulates to \(((1+i)^{36}-1)/i = 38.1411\) dollars by the end, so the required deposit is $17,750.27 / 38.1411 = $465.38 a month.

Rounded, that is $465 a month. Worth noticing: you deposit $16,754 and the head start is $2,000, so interest contributes only $1,246 — about 6.2% of the goal. Over 3 years at 4%, the saving does the work and the account is mostly a safe place to keep score. Stretch the same math over decades and the shares reverse.

Assumptions and limits

• The APY is constant for the whole period. Real savings rates float with the market — today's 4% is not a promise, so revisit the number when your bank reprices.
• Deposits are constant and monthly, landing at the end of each month. Depositing at the start of each month would earn one extra month of interest per deposit and shave the required amount slightly.
• No tax is modeled. Interest on ordinary savings is taxable income in the year it is credited, so the after-tax balance runs a little behind the chart — the questions below put a number on it.
• The goal is not inflation-adjusted. Over 3 years that barely matters; over 10 it does — a $20,000 goal a decade out buys meaningfully less when you arrive, so either aim higher or rerun this yearly with an updated goal.
• This is arithmetic, not advice: it shows what the inputs imply, not where your money should live.

Questions people ask

Where should money for a goal like this live?

The usual mapping is by horizon, descriptively: money needed within a year or two tends to sit in high-yield savings accounts, where it stays liquid and federally insured; money with a fixed date a few years out is often put in CDs or Treasury bills maturing near that date, which lock today's rate in exchange for locking the money up; and only money five-plus years out is commonly exposed to markets, because a bad year close to the deadline cannot be waited out. What fits your situation depends on facts a calculator cannot see.

Does the APY really matter for a short goal?

Less than the marketing suggests. On the default numbers, a 0% account needs ($20,000 − $2,000) / 36 = $500 a month; the 4% account needs $465 — the yield saves about $35 a month, and interest covers just 6.2% of the goal. Chasing an extra half-point of APY on a 3-year goal changes the answer by a few dollars. The rate becomes decisive only when the horizon stretches to decades, where the exponent has room to work.

What if I can't save that much a month?

The lever that actually moves the number is time. Stretch the default goal from 3 years to 4 and the required deposit falls from $465 to $340 a month — about $125 of breathing room, partly because there are more months and partly because every deposit compounds longer. The other levers are trimming the goal itself or growing the head start.

Is it better to deposit weekly instead of monthly?

It is very slightly better, because money arrives sooner and compounds a little longer — but at savings-account rates the difference over a few years is pocket change. The honest reason to pick weekly is cash-flow psychology: $465 a month is about $107.40 a week, and smaller automatic transfers are easier to leave alone. Match the transfer to your paycheck rhythm and let it run.

Is the interest I earn along the way taxed?

Yes. Interest from savings accounts, CDs and money market accounts is ordinary taxable income in the year it is credited, reported on a 1099-INT, even if you never withdraw it. In a 22% bracket a 4% APY keeps about 3.1% after federal tax, so the true required deposit is a touch higher than the pre-tax math shows — a small correction here, since interest carries so little of a short goal anyway.