Methodology

This page shows how each tool computes its numbers so you can check them in a spreadsheet. The home-page calculator, the savings-duration tool and the sequence example are covered below. Percentages you type (for example 5) are converted to decimals (0.05) before use. Amounts are in nominal dollars.

1. Savings-duration tool and sequence example

Used on how long will my savings last and sequence of returns. Year t = 0 is the first year after the start age; t = 1 is the second, and so on. Income amounts are entered in the dollars of your first withdrawal year, so they rise with inflation both before and after they start. The withdrawal-rate table uses planned first-year spending = rate x starting savings, raised by inflation each year, with no income; when a tax rate is entered, the gross amount taken from savings is larger than that spending (spending / (1 - tax rate)). For each year:

growth      = opening balance x (return - fees)
spending    = monthly spending x 12 x (1 + inflation)^t
income      = sum over income streams of monthly x 12 x (1 + inflation)^t,
              counted only in years from the stream's start age up to (not including) its end age
from savings = max(0, spending - income)
tax          = from savings x tax rate / (1 - tax rate)    (0 when no tax rate is entered)
available   = opening balance + growth + income
closing     = max(0, available - spending - tax)

A year counts as fully funded when available is at least spending plus tax. The first year in which it is not is the year the money runs short. In the sequence example the return differs each year (it is that year's value from the list below), fees are zero and benefits are zero. In the savings-duration tool the return is the same every year.

Annual time steps: the return is applied to the opening balance, then spending is withdrawn and income is added at year end.
Year 1 uses your amounts as entered; spending and income both rise with the inflation rate from year 2 (income is treated as fully cost-of-living adjusted, including before it starts).
Fees are subtracted from the return every year.
The balance cannot go below zero. "Runs short" means that year's spending could not be fully paid, so the balance is zero at year end. Spending that is exactly covered counts as funded.
Optional tax: one flat percentage you enter, applied only to money taken from savings (spending minus income, grossed up). Income is treated as already after tax. It is a simplification, not a tax calculation.
Required minimum distributions, account types and one-off costs are not modelled.
In the savings-duration tool the return is the same every year, so it shows the arithmetic of your inputs, not a forecast. The sequence example instead uses a different return each year.

2. Home-page calculator

It uses a separate, simpler model. Each year of saving, then each year of retirement:

annual savings = income x savings rate (flat, not increased over time)
saving year:      balance = balance x (1 + return) + annual savings
shortfall         = retirement spending - Social Security - other income
retirement year n (n = 1 is the first year of retirement): balance = balance x (1 + return) - shortfall x (1 + inflation)^(n - 1)

Savings are reported as lasting until the last age at which the balance has not gone below zero (exactly zero counts as funded). The "rule-of-thumb monthly income" card is separate: 4% of the balance at retirement divided by 12, plus Social Security and other income. The "you need X more" figure uses the same convention: it adds up, for each retirement year n, the shortfall x (1 + inflation)^(n - 1) divided by (1 + return)^n, which is the balance needed at retirement for the model to just reach life expectancy, and compares it with the projected balance. This model has no fees, taxes or account types. The spending and Social Security amounts you enter are treated as amounts for your first year of retirement; the shortfall is multiplied by (1 + inflation)^(n - 1), so year 1 uses the amounts as entered and year 2 is inflated once (default: $60,000 - $20,000 = $40,000 in year 1, $41,200 in year 2). Nothing is inflated between today and retirement, and the return you enter is nominal.

Cross-check: both tools give the same answer

Take $500,000 at age 65, spending $60,000 a year ($5,000 a month), Social Security $24,000 a year ($2,000 a month), a 5% return, 2.5% inflation and no fees. The home-page calculator (with the starting savings set so the balance at 65 is $500,000) and the savings-duration tool (fees set to 0) both show spending fully funded through age 82 and the money running short at age 83. Both tools use the same convention: year 1 as entered, inflation from year 2.

3. Sequence-of-returns example data

The example uses 30 invented yearly returns (in percent): 22, 15, 9, 18, -8, 12, 6, -15, 24, 3, 10, -22, 14, 7, 19, -4, 11, 1, -12, 20, 8, 13, -6, 16, 2, -18, 21, 5, 9, -3. They are not market history. The three orders are the list sorted high to low, as written, and sorted low to high. The CSV download has every year's return and balance.

Limits

Results are arithmetic on the inputs you choose, not predictions.
The tools do not use historical market data or random simulation.
Tax rules, account types, required minimum distributions, Medicare and Social Security claiming rules are not modelled (the savings-duration tool has one optional flat tax percentage that you enter); ask a qualified professional about them.

Corrections

If a result does not match your spreadsheet, email support@retirement-calculator.app with your inputs and we will check it.