The formula
Payout = capital × i / (1 − (1 + i)⁻ⁿ)
Where it comes from
It is the loan payment formula with the roles reversed: here the bank pays you. The capital keeps earning interest while it is being drawn down, so the payout you can take is larger than simply splitting the capital across the months. The gap between the two figures shown is exactly that: the interest the capital earns along the way.
How to work it out by hand
- Note the capital, the annual rate and the years you want to draw it
- Convert the rate to monthly by dividing by twelve
- Apply the payment formula with those figures
- Compare with the capital divided by the months: the gap is the interest
What is worth knowing
This is financial arithmetic, not an insurer's annuity. A real annuity is priced on life expectancy rather than a chosen term, carries charges and has its own tax treatment in every country, so the real figure will be lower. The rate you enter matters a great deal too: it is what the capital is assumed to earn for all those years, and assuming it high is the easiest way to come up short.