# Savings Withdrawal Calculator

> Given a balance earning a monthly-compounded return, computes how many months a fixed monthly withdrawal lasts (and the total withdrawn and interest earned), or the level monthly withdrawal that exhausts the balance over a chosen number of years, plus the interest-only withdrawal that preserves the balance forever.

- Calculator id: `savings-withdrawal` · Category: Finance (`finance`) · Tool name: `calculate_savings_withdrawal`
- Canonical page: https://tttkmbb.com/finance/savings-withdrawal · This document: https://tttkmbb.com/finance/savings-withdrawal.md · JSON definition: https://tttkmbb.com/finance/savings-withdrawal.json

## Purpose

Given a balance earning a monthly-compounded return, computes how many months a fixed monthly withdrawal lasts (and the total withdrawn and interest earned), or the level monthly withdrawal that exhausts the balance over a chosen number of years, plus the interest-only withdrawal that preserves the balance forever.

**Use when:** You are drawing down savings, a retirement account or an inheritance and want either the depletion date for a given withdrawal or the affordable withdrawal for a given period.

**Do not use when:** You want the required portfolio for a withdrawal rate (use fire-number) or are still accumulating (use retirement-savings or compound-interest).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `balance` | number |  | required | Amount available at the start. (> 0, max 1000000000000) |
| `annual_return_percent` | number | % | required | Nominal annual return in percent, compounded monthly. (min 0, max 50) |
| `monthly_withdrawal` | number |  | optional | Fixed amount withdrawn at the end of every month; enables the how-long-it-lasts result. (> 0, max 1000000000) |
| `years` | number | years | optional | Enables the sustainable monthly withdrawal that empties the balance after exactly this many years. (> 0, max 100) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `perpetual_monthly_withdrawal` | number |  | balance × annual_return_percent / 1200: taking only this each month never touches the principal. |
| `months_lasting` | integer | months | Number of monthly withdrawals until the balance is exhausted (includes the smaller final one); only for monthly_withdrawal. |
| `duration` | string |  | months_lasting in years and months, or 'indefinitely' when the withdrawal does not exceed monthly interest. |
| `total_withdrawn` | number |  | Sum of all withdrawals until depletion. |
| `total_interest_earned` | number |  | total_withdrawn − balance. |
| `final_withdrawal` | number |  | The last, usually smaller, withdrawal that empties the account. |
| `sustainable_monthly_withdrawal` | number |  | Level withdrawal that exhausts the balance after exactly `years` (only when years is given). |
| `sustainable_total_withdrawn` | number |  | sustainable_monthly_withdrawal × 12 × years. |

## Formula

`i = annual_return_percent/1200. Duration: months = −ln(1 − i × balance / monthly_withdrawal) / ln(1 + i), rounded up (balance / withdrawal if i = 0); no finite duration if monthly_withdrawal ≤ balance × i. Sustainable withdrawal over n = 12 × years months: W = balance × i / (1 − (1 + i)^−n).`

Ordinary-annuity arithmetic: interest is credited monthly on the remaining balance and withdrawals are taken at month end (the same formula as a loan payment with the roles reversed). Returns are assumed constant; inflation and taxes are ignored.

## Data Sources

- Wikipedia – Amortization calculator (annuity payment formula) — https://en.wikipedia.org/wiki/Amortization_calculator (reference, retrieved 2026-09-24)
- Wikipedia – Annuity — https://en.wikipedia.org/wiki/Annuity (reference, retrieved 2026-09-24)
- Wikipedia – Trinity study (safe withdrawal rates) — https://en.wikipedia.org/wiki/Trinity_study (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/savings-withdrawal?balance=…&annual_return_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/savings-withdrawal` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/savings-withdrawal · OpenAPI operationId `calculate_savings_withdrawal` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "savings-withdrawal", "inputs": {…}}`

## Example

- 500,000 at 5 %, withdraw 3,000 per month: inputs `{"balance":500000,"annual_return_percent":5,"monthly_withdrawal":3000}` → `{"perpetual_monthly_withdrawal":2083.33,"months_lasting":286,"duration":"23 years 10 months","total_withdrawn":855427,"total_interest_earned":355427,"final_withdrawal":427}`
- 300,000 at 4 % to last 20 years: inputs `{"balance":300000,"annual_return_percent":4,"years":20}` → `{"perpetual_monthly_withdrawal":1000,"sustainable_monthly_withdrawal":1817.94,"sustainable_total_withdrawn":436305.84}`

```
GET https://tttkmbb.com/api/v1/calculate/savings-withdrawal?balance=500000&annual_return_percent=5&monthly_withdrawal=3000
```

## Limitations

You want the required portfolio for a withdrawal rate (use fire-number) or are still accumulating (use retirement-savings or compound-interest). Ordinary-annuity arithmetic: interest is credited monthly on the remaining balance and withdrawals are taken at month end (the same formula as a loan payment with the roles reversed). Returns are assumed constant; inflation and taxes are ignored. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why does the money last so long at 5 %?**

Interest on 500,000 at 5 % is about 2,083 per month, so a 3,000 withdrawal only draws the principal down by about 917 at first; the drawdown accelerates as the balance and its interest shrink.

**Should I use a real or nominal return?**

If the withdrawal should keep its purchasing power, enter a real return (nominal minus inflation) and treat the withdrawal as today's money; otherwise the fixed nominal withdrawal buys less each year.

## Related

- [FIRE Number Calculator](https://tttkmbb.com/finance/fire-number.md) — Portfolio needed for a chosen withdrawal rate.
- [Retirement Savings Calculator](https://tttkmbb.com/finance/retirement-savings.md) — Grow the balance before drawing it down.
- [Loan Payment Calculator](https://tttkmbb.com/finance/loan-payment.md) — The same annuity formula applied to a loan.