Savings Goal Calculator
Reach a savings target: enter a goal, current balance and expected return to get the monthly amount to save, or how long a fixed deposit takes.
Set a savings target, your starting balance and an expected return. Choose a deadline to get the monthly amount to save, or a monthly amount to get the time it takes to arrive.设定一个储蓄目标、初始余额与预期回报。选「按期限」得出每月应存金额，或选「按供款」得出达成目标所需的时间。
Fill in the fields to plan the goal.填入各字段即可规划目标。
- Still to save尚需储蓄
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- Total you contribute你的供款总额
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- Growth from returns回报带来的增长
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- Time to reach达成所需时间
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To reach a savings goal by a set date, you save the gap between your goal and where compounding will carry your current balance, spread over the months — as a level monthly deposit. Flip the question and a fixed monthly deposit tells you how long the goal takes instead. The expected return does the quiet work: the higher it is, the less of the goal your own deposits have to cover.要在设定的日期达成储蓄目标，你需要填补目标金额与「复利把当前余额带到的水平」之间的缺口，并把它摊到各个月份——即一笔固定的每月存款。把问题反过来，一笔固定的每月存款则告诉你达成目标需要多久。预期回报在暗中发力：回报越高，需要靠你自己存款覆盖的部分就越少。
01The formula公式
By date — solve the deposit c:按期限——求解每月存款 c：
c = ( Goal − Current × (1+i)m ) × i ÷ ( (1+i)m − 1 )c = ( 目标 − 当前 × (1+i)m ) × i ÷ ( (1+i)m − 1 )
when i = 0: c = ( Goal − Current ) ÷ m当 i = 0 时：c = ( 目标 − 当前 ) ÷ m
By contribution — solve the months m:按供款——求解月数 m：
m = ln( (Goal·i + c) ÷ (Current·i + c) ) ÷ ln(1+i)m = ln( (目标·i + c) ÷ (当前·i + c) ) ÷ ln(1+i)
when i = 0: m = ( Goal − Current ) ÷ c当 i = 0 时：m = ( 目标 − 当前 ) ÷ c
This treats deposits as arriving at the end of each month (an ordinary annuity) and the return as compounding monthly. It is the same future-value machinery as a savings account or a systematic investment plan, run in reverse to find the missing piece.这里把存款视为在每月末存入（普通年金），回报按月复利。它与储蓄账户或定期定额投资计划背后的终值公式相同，只是反过来求那个缺失的量。
02A worked example一个算例
Suppose your goal is $100,000, you already hold $10,000, you expect 6% a year, and you want to arrive in 10 years.假设你的目标是 $100,000，已经持有 $10,000，预期年回报 6%，希望在 10 年内达成。
- i = 6 ÷ 100 ÷ 12 = 0.005, m = 10 × 12 = 120i = 6 ÷ 100 ÷ 12 = 0.005， m = 10 × 12 = 120
- (1+i)m = 1.005120 ≈ 1.8194(1+i)m = 1.005120 ≈ 1.8194
- Your $10,000 grows to 10,000 × 1.8194 ≈ $18,194 on its own你的 $10,000 自行增长到 10,000 × 1.8194 ≈ $18,194
- c = (100,000 − 18,194) × 0.005 ÷ 0.8194 ≈ $499 per monthc = (100,000 − 18,194) × 0.005 ÷ 0.8194 ≈ $499 每月
Over the ten years those deposits add up to about $59,900, your starting balance is $10,000, and the remaining ~$30,100 is growth the return did for you — roughly a third of the goal you never had to deposit.十年间这些存款累计约 $59,900，起始余额 $10,000，其余 约 $30,100 是回报替你创造的增长——约占目标的三分之一，是你无需存入的部分。
03The common trap常见陷阱
A single return number pretends the market delivers the same percentage every month. Real returns arrive in a jagged sequence — a rough early stretch, when the balance is small, hurts far less than a rough stretch near the deadline, when the balance is large. Two plans with the same average return can land in very different places. Treat the return as a planning assumption, not a promise, and revisit the deposit as the real balance drifts from the smooth curve.单一的回报数字假装市场每个月都交出相同的百分比。真实回报以参差的序列出现——余额还小时的早期低迷，远不如临近期限、余额已大时的低迷伤人。两个平均回报相同的计划，可能落到截然不同的位置。把回报当作一项规划假设，而非承诺；当实际余额偏离这条平滑曲线时，及时调整每月存款。
04Where this breaks它的局限
The math plans one goal on clean assumptions. A few honest limits:这套算法在干净的假设下规划单一目标。几点诚实的局限：
- Inflation. A $100,000 goal set today buys less in ten years. If the goal is a future cost, either grow the target for inflation or read the expected return as a real (after-inflation) rate.通胀。今天设定的 $100,000 目标，十年后能买的东西更少。若目标是一笔未来的支出，要么按通胀上调目标，要么把预期回报理解为实际（扣除通胀后）利率。
- Taxes and fees. Returns in a taxable account are trimmed by tax on gains, and fund fees quietly lower the rate that actually compounds. The plan uses the gross rate you type in.税与费用。应税账户中的回报会被收益税削减，基金费用也会悄悄拉低真正参与复利的利率。本计划使用你输入的毛回报率。
- Timing of deposits. This assumes deposits at each month’s end. Depositing at the start of the month, or contributing yearly instead of monthly, shifts the answer slightly.存款时点。这里假设在每月末存入。若在月初存入，或按年而非按月供款，答案会略有变化。
Compounding covers part of any long goal — the longer the horizon and the higher the return, the smaller the slice you have to deposit yourself.复利会覆盖任何长期目标的一部分——期限越长、回报越高，需要你亲自存入的那一份就越小。
See how a balance grows deposit by deposit with the 用 compounding calculator复利计算器, or turn a start and end value into a rate with the 看余额如何随每笔存款增长，或用 CAGR calculator复合年增长率计算器.把起止金额换算成回报率。