Quick answer: 500,000 earning 5% a year pays 3,299.78 a month for 20 years; taking 3,000 a month instead makes it last 23.76 years.
How it's calculated
The payout that uses up a lump sum L in n periods is W = L·i ÷ (1 − (1 + i)^−n), where i is the annual return divided by payouts a year. Paid at the start of each period, divide by (1 + i). The return is treated as a nominal yearly rate; if yours is an effective yearly rate, the payout is a little lower (3,269.18 instead of 3,299.78 a month for 500,000 at 5% over 20 years).
At a chosen payout W, the sum lasts n = −ln(1 − L·i ÷ W) ÷ ln(1 + i) periods. If W is no more than the return L·i, the balance never falls and the money lasts indefinitely.
Insurance annuities for life work differently: they pool longevity risk and depend on age and the insurer's rates. To build the lump sum, see the annuity calculator and the retirement calculator.
Worked examples
- 500,000 at 5%, monthly, 20 years: W = 3,299.78 a month
- 500,000 at 5%, 3,000 a month: n = 285.1 months = 23.76 years
Frequently asked questions
What return should I assume in retirement?
A cautious one, since withdrawals during a market fall do lasting damage. Many plans use a rate close to deposit or sukuk yields for the income part.
Does it allow for inflation?
No; the payout is the same each period. To keep buying power, plan a payout that rises, which means a lower starting amount.
What is the payout that never runs out?
The return the sum earns each period. Taking only that keeps the lump sum intact.
Why does money last longer at a higher return?
The remaining balance keeps earning while you withdraw, so more of each payout comes from growth. A return that falls short of your assumption shortens the time, so test a lower one too.
Is it better to be paid at the start or end of a period?
Being paid at the start gives you money sooner, so each payout is a little smaller for the same lump sum and term.
Does this include fees or tax?
No. It works from the return you enter, so use a figure after any fees and adjust for tax if it applies to you.