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Annuity Income Calculator

See the income a lump sum annuity can pay you.

How it is calculated

This is a fixed-term annuity: the lump sum is paid out in equal instalments that also earn interest on what is still left. Formula: i = annual_rate / 100 / m, n = years × m, payment = P × i / (1 − (1 + i)−n), where P is the principal in dollars, m the payments per year (12 monthly, 4 quarterly, 1 yearly) and n the total number of payments. At a 0% rate the payment is just P / n. Total income is payment × n. The principal must not be negative; years and payments per year must be above zero. There is no life expectancy, fee or tax in the maths, so a real life annuity quote will differ.

Worked example

Principal 250000, 5% a year, 20 years, 12 payments a year. Periodic rate i = 5 / 100 / 12 ≈ 0.004167, and n = 20 × 12 = 240. The factor (1 + i)−240 is about 0.3686, so the denominator is 1 − 0.3686 = 0.6314. Payment = 250000 × 0.004167 / 0.6314 = $1,649.89 a month. Over 240 payments the total income is $395,973.44.

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Common mistakes

  • Reading the result as a lifetime income. The engine pays out the principal over exactly the years you enter, then stops; it does not model how long you will live.
  • Setting payments per year to 12 but thinking of the years field as months. Years is in years, so 20 years gives 240 payments.
  • Entering the rate as a decimal (0.05) instead of a percentage (5).
  • Comparing the total income with an insurer's quote without allowing for the insurer's fees, taxes and mortality assumptions, which the formula leaves out.
  • Changing payments per year and forgetting that the same annual rate is then split over more or fewer periods, which slightly changes the total.

Sources

About this calculator

An immediate annuity converts a lump-sum principal into a stream of regular income payments, typically for a fixed period or for life, in exchange for handing the principal over to an insurer. This calculator covers the fixed-period case and works the amortization math in reverse from a standard loan payment formula: given the principal, the annual interest rate, the number of years and the payments per year, it solves for the level periodic income amount that pays the principal down to zero over that term, PMT = PV × r / [1 − (1 + r)^(−n)].

Retirees use immediate annuities to turn a 401(k) rollover or a windfall like an inheritance into predictable monthly income, trading investment flexibility for payment certainty. This calculator does not model lifetime payouts, and because insurers price annuities using their own actuarial assumptions and fees, it gives you a baseline fixed-term income figure to sanity-check against any quote an insurance company offers.

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