Annuity Calculator
Turn a lump sum into a stream of equal payments, or find the lump sum a desired payment needs, using the present value of an annuity at a chosen rate and term.
Comment utiliser cette calculatrice
- 1Choose whether you have a lump sum and want the payment, or a target payment and want the lump sum.
- 2Enter that amount, the interest rate, and the payout period in years.
- 3Choose how often payments are made.
- 4Read the payment (or required lump sum), the total paid out, and the interest earned.
Comment ça marche
Present value of an annuity
PV = PMT × (1 − (1 + i)⁻ⁿ) ÷ i PMT = PV × i ÷ (1 − (1 + i)⁻ⁿ) i = annual rate ÷ payments per year n = years × payments per year
An annuity is a series of equal payments over time, and its present value is the single lump sum today that is financially equivalent to that whole stream, given an interest rate. The annuity factor — the bracketed term — bundles the discounting of every future payment into one multiplier. To find the payment a lump sum can support, divide the lump sum by the factor; to find the lump sum a desired payment needs, multiply the payment by the factor. Because the money still earning interest between payments keeps working, the total of all payments made is larger than the starting lump sum, and the difference is the interest earned over the payout period. This is the core arithmetic behind pension payouts, structured settlements, and retirement withdrawal plans.
Exemple détaillé
A $500,000 lump sum paid out monthly over 20 years while the balance earns 5% a year supports about $3,300 a month. Over the 240 payments that totals roughly $792,000 — the extra $292,000 above the original half-million is the interest the shrinking balance keeps earning as it is drawn down.
Annuity Calculator : le guide complet
What an annuity really is
At its heart, an annuity is just a stream of equal payments spread over time, and the central question is always how it relates to a single lump sum. A pension that pays a fixed amount each month, a lottery paid in yearly instalments, a loan repaid in equal payments, and a retirement account drawn down steadily are all annuities in the mathematical sense. The present-value formula ties the two views together: it says exactly how much a promised stream of future payments is worth as one amount today, and vice versa.
The reason a lump sum and a payment stream are not simply equal is the time value of money. A dollar received years from now is worth less than a dollar today, because today's dollar could be invested in the meantime. The annuity factor discounts each future payment by how far away it is and adds them up. This is why $500,000 today does not translate into $500,000 divided evenly over twenty years — the balance keeps earning interest as it is paid out, so it supports meaningfully larger total payments.
Payout annuities and the drawdown problem
One of the most practical uses of this maths is the retirement drawdown: you have saved a lump sum and want to know how much you can take each month so that it lasts a fixed number of years. This is the 'payment from a lump sum' mode. The answer depends heavily on the interest rate the remaining balance earns — a higher assumed return supports a larger payment, because the money left in the account works harder between withdrawals.
This fixed-term approach differs from the 4% rule and other perpetual-withdrawal strategies in an important way: it deliberately draws the balance to zero at the end of the term. That is efficient if you know your horizon, but risky if you outlive it, since the payments simply stop. Lifelong annuity products solve this by pooling longevity risk across many people, guaranteeing payments until death — at the cost of insurer fees and giving up the lump sum. The calculator shows the underlying fixed-term maths, which is the foundation those products are priced on.
Lump sum or payments? Reading the trade-off
People often face a real version of this question: a pension or settlement offers a choice between a lump sum now and a stream of payments over time. The present-value calculation is exactly the tool for comparing them. Compute the lump sum that the offered payment stream is worth at a realistic interest rate, and compare it to the lump sum on the table. If the offered lump sum is larger, taking it and investing yourself may win; if the payment stream's present value is larger, the payments are the better deal on paper.
The comparison hinges entirely on the rate you assume, which is a judgement about what return you could earn and how safe it is. A higher assumed rate lowers the present value of the payments, favouring the lump sum; a lower rate favours the payments. Beyond the maths, there are real considerations the formula cannot weigh: a payment stream protects against overspending and market crashes but exposes you to inflation and the provider's solvency, while a lump sum offers control and flexibility but demands discipline. Use the numbers to frame the decision, then layer these human factors on top.
Questions fréquentes
How much income will a lump sum provide?
It depends on the interest rate and payout period. A $500,000 lump sum paid monthly over 20 years while earning 5% supports about $3,300 a month. The balance keeps earning interest as it's drawn down, so total payments exceed the original lump sum.
What is the present value of an annuity?
It is the single lump sum today that equals a stream of future payments, given an interest rate. Because future money is worth less than money now, the formula discounts each payment. It lets you compare a lump-sum offer against a payment stream on equal terms.
Should I take a lump sum or annuity payments?
Compare the present value of the payments at a realistic rate against the lump sum offered. A higher assumed return favours the lump sum; a lower one favours the payments. Beyond the maths, weigh inflation, provider solvency, spending discipline, and how long you expect to live.
Does this calculator include annuity fees?
No — it shows the underlying financial maths of a fixed-term annuity, without the insurer fees, commissions, or guarantees a real annuity product carries. It also assumes a fixed term rather than lifelong payments. Use it to understand the mechanics, not as a product quote.