# Retirement calculator

> Calculate how much you need to retire on inflation-adjusted expenses, the monthly saving that gets you there, and how the money runs down.

交互版本：https://www.calcopenly.com/zh/finance/retirement-calculator
主题：财务计算器

The plan works backwards from spending. Today's monthly expenses are grown by inflation to the retirement date. The corpus is the value at retirement of withdrawals that start at that amount and rise with inflation every month until the planning age, discounted at the return you expect during retirement. Your current savings are grown to retirement, and a monthly saving, invested at the start of each month, closes the rest of the gap.

With the defaults, age 30, retiring at 60 and planning to 85, expenses of 4,000 a month become 9,709.05 at 3% inflation. Funding 25 years of rising withdrawals at a 5% return needs a corpus of 2,314,301.01, or 953,461.37 in today's money. The 50,000 already saved grows to 380,612.75 at 7%, and saving 1,644.20 a month covers the rest.

Returns and inflation are held constant. Taxes, pensions and Social Security are not modeled, so subtract any guaranteed income from the expenses before you enter them.

## How the corpus is calculated, step by step

Take someone aged 35 who wants to retire at 65 and plan to 90, on 3,000 a month at today's prices, with 2.5% inflation, a 6% return while saving, 4% during retirement and 40,000 already saved.

1. Spending at retirement: 3,000 × 1.025^30 = 6,292.70 a month.
2. Monthly rates that compound exactly to the yearly ones: g = 1.025^(1/12) − 1 = 0.20598% for inflation and j = 1.04^(1/12) − 1 = 0.32737% for the return.
3. Ratio of one month's withdrawal to the next, in present-value terms: q = (1 + g) ÷ (1 + j) = 0.998790. Over 300 months, q^300 = (1.025 ÷ 1.04)^25 = 0.695446.
4. Corpus, the sum of 300 rising withdrawals discounted to age 65: 6,292.70 × (1 − 0.695446) ÷ (1 − 0.998790) = 1,583,935.15.
5. Current savings at 65: 40,000 × 1.06^30 = 229,739.65, leaving a gap of 1,354,195.51.
6. Monthly saving: the gap divided by the value of 360 start-of-month deposits of 1 at i = 1.06^(1/12) − 1, which is 979.2565, gives 1,382.88.

At today's prices the corpus is 755,129.50. It is also 21.0 times a year of spending at the first month's rate (12 × 6,292.70 = 75,512.43), and that multiple is what rules of thumb such as the 4% rule state.

## Corpus as a multiple of annual spending

The corpus depends on only two things once spending is fixed: the years in retirement and the real return, which is (1 + return) ÷ (1 + inflation) − 1. The worked example's 4% return and 2.5% inflation give 1.46% real. The table shows the corpus as a multiple of 12 first-month withdrawals, for withdrawals that rise with inflation and are taken at the start of each month:

| Years in retirement | 0% real | 1% real | 2% real | 3% real | 4% real |
|---|---|---|---|---|---|
| 20 | 20.0 | 18.1 | 16.5 | 15.1 | 13.9 |
| 25 | 25.0 | 22.1 | 19.7 | 17.7 | 16.0 |
| 30 | 30.0 | 25.9 | 22.6 | 19.9 | 17.7 |
| 35 | 35.0 | 29.6 | 25.3 | 21.8 | 19.1 |
| 40 | 40.0 | 33.0 | 27.7 | 23.5 | 20.2 |

Dividing 1 by the multiple gives the first-year withdrawal rate. The 4% rule's multiple of 25 funds 30 years only if the portfolio earns a steady 1.27% above inflation, or 40 years at 2.61%. That is well below what stocks and bonds have averaged, and the gap is deliberate, as the next section explains.

## The 4% rule: where it comes from and where it breaks

William Bengen, a financial planner, tested withdrawal rates against actual US returns and inflation for retirements starting in each year from 1926 ([Journal of Financial Planning, October 1994, reprinted 2004](https://www.financialplanningassociation.org/sites/default/files/2021-04/MAR04%20Determining%20Withdrawal%20Rates%20Using%20Historical%20Data.pdf)). His portfolio was half common stocks and half intermediate-term Treasury notes, continually rebalanced, with all assets in tax-deferred accounts. A first-year withdrawal of 3%, raised with inflation each year, never lasted less than 50 years. At 4% no portfolio ran out in under 33 years, while 4.25% could run out in 28.

The paper opens with a fictional planner who expects a 60/40 portfolio to keep earning its historical 8.2% a year, subtracts 3% inflation and lets clients draw the 5% real return. Bengen calls that a fallacy: average returns and average inflation are not a sound basis for a safe withdrawal rate, because a severe market fall combined with high inflation can drain a portfolio first. In his data, people who retired in the late 1960s and early 1970s would have had only about 20 years of income at 5%, after the 1973–74 crash hit during high inflation. This calculator also assumes constant averages, so treat its corpus as a minimum and use a cautious return for the retirement years.

The rule has limits of its own:

- It rests on one country's history, and nothing guarantees future returns will match it.
- It ignores fees and taxes. A 1% yearly fee comes straight off the return, which can move you a full column to the left in the table above.
- It targets 30 years. Someone retiring at 50 who plans to 95 needs 45 years, and at 2% real even 40 years needs 27.7 times spending, a 3.6% first-year rate.

## What today's spending will cost later

Inflation compounds exactly like interest. What 1,000 a month of spending today will cost:

| Inflation | After 10 years | After 20 years | After 30 years | After 40 years |
|---|---|---|---|---|
| 2% | 1,218.99 | 1,485.95 | 1,811.36 | 2,208.04 |
| 3% | 1,343.92 | 1,806.11 | 2,427.26 | 3,262.04 |
| 4% | 1,480.24 | 2,191.12 | 3,243.40 | 4,801.02 |
| 6% | 1,790.85 | 3,207.14 | 5,743.49 | 10,285.72 |

Central bank targets give a starting point for the inflation field. The [US Federal Reserve](https://www.federalreserve.gov/faqs/economy_14400.htm), the [Bank of England](https://www.bankofengland.co.uk/monetary-policy/inflation) and the [European Central Bank](https://www.ecb.europa.eu/mopo/strategy/html/index.en.html) target 2%. The [Reserve Bank of India](https://www.rbi.org.in/Scripts/FS_Overview.aspx?fn=2752) targets 4% CPI inflation within a 2% to 6% band, a target the government retained in March 2026 for April 2026 to March 2031. Targets are not forecasts: US consumer prices rose 3.4% in the year to August 2026 ([BLS CPI](https://www.bls.gov/cpi/)). A plan that holds up at a point or two above target is safer than one built on the target itself.

## Monthly saving needed for every 1,000,000

The saving required to build 1,000,000, deposited at the start of each month from zero, at three yearly returns:

| Years to retirement | 4% return | 6% return | 8% return |
|---|---|---|---|
| 10 | 6,794.58 | 6,125.04 | 5,516.23 |
| 15 | 4,074.02 | 3,468.51 | 2,943.09 |
| 20 | 2,739.48 | 2,194.69 | 1,746.24 |
| 25 | 1,958.81 | 1,471.50 | 1,093.09 |
| 30 | 1,454.52 | 1,021.18 | 705.41 |
| 35 | 1,107.59 | 724.49 | 463.75 |
| 40 | 858.47 | 521.66 | 308.47 |

Scale by your own gap: a 1,354,195.51 gap over 30 years at 6% needs 1.3542 × 1,021.18 = 1,382.88 a month, the worked example's answer. In this table, starting ten years earlier cuts the monthly amount by 41% to 68%.

## Mistakes that distort the plan

- **A retirement return copied from the saving years.** If you will hold more bonds and cash once withdrawals start, the return during retirement should sit below the return before it.
- **Returns quoted before fees.** Enter what you expect to keep.
- **A planning age set at life expectancy.** Life expectancy is an average, so many people live past it. Plan to an age you are unlikely to pass.
- **A pension that starts after you retire.** UK State Pension age is 66 for people born before 6 April 1960 and rises to 67 between 2026 and 2028. If you stop work before your pension starts, run the plan once with full expenses for the gap years and again with expenses net of the pension from the date it begins.

To turn the monthly saving into a fund investment plan with yearly increases, use the [SIP calculator](/zh/finance/sip-calculator). The [inflation calculator](/zh/finance/inflation-calculator) converts any figure between today's money and future money, and the [savings goal calculator](/zh/finance/savings-goal-calculator) solves for the time needed at a saving you can afford.

## 输入

- **Current age**
- **Retirement age**
- **Plan until age**: Planning to a later age covers the risk of outliving your savings
- **Monthly expenses today**: What your retirement lifestyle would cost per month at today's prices
- **Inflation (per year)**
- **Return before retirement (per year)**
- **Return during retirement (per year)**
- **Savings so far**

## 结果

- Corpus needed at retirement — 主要结果
- Monthly savings needed
- Monthly expenses when you retire
- Current savings grown to retirement
- Gap to fill by saving
- Corpus in today's money
- Years until retirement
- Years in retirement

## 公式

$$
\text{Corpus} = E_R\,\frac{1 - q^{12H}}{1 - q},\quad q = \frac{1+g}{1+j},\quad E_R = E(1+\pi)^{Y}
$$

## 计算示例

### Age 30, retire at 60, plan to 85

- Current age: 30 years
- Retirement age: 60 years
- Plan until age: 85 years
- Monthly expenses today: 4000
- Inflation (per year): 3%
- Return before retirement (per year): 7%
- Return during retirement (per year): 5%
- Savings so far: 50,000
- **Corpus needed at retirement: 2,314,301.01**
- **Monthly savings needed: 1,644.20**
- **Monthly expenses when you retire: 9,709.05**
- **Current savings grown to retirement: 380,612.75**
- **Corpus in today's money: 953,461.37**
- 核验来源：Python decimal (prec 50) month-by-month sum of discounted start-of-month withdrawals, and a simulated start-of-month deposit schedule

### Return in retirement equals inflation

- Current age: 40 years
- Retirement age: 60 years
- Plan until age: 80 years
- Monthly expenses today: 1000
- Inflation (per year): 6%
- Return before retirement (per year): 8%
- Return during retirement (per year): 6%
- Savings so far: 0
- **Corpus needed at retirement: 769,712.51**
- **Corpus in today's money: 240,000.00**
- **Monthly savings needed: 1,344.10**
- 核验来源：Python decimal: when return = inflation the corpus is 240 months × first withdrawal 1000 × 1.06²⁰ = 769,712.51; 240,000 in today's money

### All rates zero

- Current age: 50 years
- Retirement age: 60 years
- Plan until age: 70 years
- Monthly expenses today: 2000
- Inflation (per year): 0%
- Return before retirement (per year): 0%
- Return during retirement (per year): 0%
- Savings so far: 40,000
- **Corpus needed at retirement: 240,000.00**
- **Gap to fill by saving: 200,000.00**
- **Monthly savings needed: 1,666.67**
- 核验来源：Hand calculation: 2000 × 120 months = 240,000; (240,000 − 40,000) / 120 = 1,666.67

### Existing savings already cover the plan

- Current age: 55 years
- Retirement age: 65 years
- Plan until age: 75 years
- Monthly expenses today: 1000
- Inflation (per year): 2%
- Return before retirement (per year): 5%
- Return during retirement (per year): 4%
- Savings so far: 500,000
- **Corpus needed at retirement: 133,060.93**
- **Current savings grown to retirement: 814,447.31**
- **Gap to fill by saving: 0.00**
- **Monthly savings needed: 0.00**
- 核验来源：Python decimal month-by-month model: 500,000 × 1.05¹⁰ = 814,447.31 exceeds the 133,060.93 needed

## 常见问题

### How much money do I need to retire?

Enough to fund your spending, rising with inflation, for as long as you plan to live. The default plan, 4,000 a month in today's money for 25 years from age 60, needs 2,314,301.01 at retirement (953,461.37 in today's money) with a 5% return and 3% inflation. Planning to age 95 instead of 85 raises the corpus to 2,970,163.44.

### What is the 4% rule for retirement?

Withdraw 4% of your savings in the first year of retirement, then raise the amount with inflation each year. William Bengen (Journal of Financial Planning, October 1994) found that this rate lasted at least 33 years in the historical US returns he tested. By that rule, spending 48,000 a year needs 48,000 ÷ 0.04 = 1,200,000 at retirement.

### How much can I put in a 401(k) and an IRA in 2026?

For 2026 the IRS limits are $24,500 for a 401(k) and $7,500 for an IRA. Workers 50 and over can add a catch-up of $8,000 to a 401(k), or $11,250 at ages 60 to 63, and $1,100 to an IRA. Contributing the full $24,500 is about 2,041.67 a month, more than the 1,644.20 the default plan needs.

### How does retiring later change how much I need to save?

Retiring later adds years of saving and growth and removes years of withdrawals. In the default plan, retiring at 65 instead of 60 cuts the monthly saving from 1,644.20 to 993.81, while retiring at 55 raises it to 2,566.99. In the US, full retirement age for Social Security is 67 for anyone born in 1960 or later.

### How does inflation affect retirement planning?

It raises both the first withdrawal and every later one. With the other defaults fixed, 2% inflation needs a corpus of 1,548,135.00 and 992.74 a month of saving; 3% needs 2,314,301.01 and 1,644.20; 4% needs 3,462,902.56 and 2,620.85. One percentage point of inflation either way changes the monthly saving by about 40% to 60% here.

### “Retirement calculator”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：4。 例如，“Age 30, retire at 60, plan to 85”根据Python decimal (prec 50) month-by-month sum of discounted start-of-month withdrawals, and a simulated start-of-month deposit schedule进行核验。

### 这种方法出自哪里？

Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (growing annuities); Microsoft Excel FV and PMT functions (type = 1, payments at the start of each period).

## 来源

- Brealey, Myers & Allen — Principles of Corporate Finance, ch. 2 (growing annuities)
- [Microsoft Excel FV and PMT functions (type = 1, payments at the start of each period)](https://support.microsoft.com/office/fv-function-2eef9f44-a084-4c61-bdd8-4fe4bb1b71b3)

_仅用于规划。贷款机构、税务机关和市场采用各自的舍入方式、费用和规则；作出承诺前，请向相关机构确认数值。_