Annuity Present Value: My Pension Offered $700,000 Now or $3,000 a Month. The Discount Rate Decided Everything
My uncle called me last month with a letter in his hand and a question he couldn't answer. His old employer's pension plan was offering him a choice: $700,000 in a single payment now, or $3,000 a month for 25 years. "That's $900,000 if I take the monthly," he said. "Obviously the monthly, right?"
Not so fast. $900,000 spread over 25 years and $700,000 today are not the same kind of money. The question is what that monthly stream is worth today, and that is an annuity present value problem. This guide is for anyone facing a pension buyout, lottery payout, structured settlement or any "lump sum or payments?" decision, and by the end you'll be able to price the choice yourself with the Annuity Calculator.
⚠️ Disclaimer
This article is for informational purposes only and does not constitute financial advice. Pension and annuity decisions can be irreversible and have tax consequences. Always consult a qualified financial adviser for your specific situation.
What Is Annuity Present Value?
Annuity present value is the single amount of money today that is equivalent to a series of equal future payments, once you account for the interest those dollars could earn in the meantime. It converts a stream of payments into one comparable number.
The idea behind it is the time value of money: a dollar in your hand today can earn interest, so a dollar promised in 2040 is worth less than a dollar now. The rate used to shrink future payments back to today's value is called the discount rate.
The mistake my uncle made, and the one I see constantly, is adding up the payments. Total payments ($900,000) ignore time entirely. It's like comparing a salary offer in 1990 and 2026 by looking at the raw numbers.
How Do You Calculate Annuity Present Value?
The standard formula for the present value of an ordinary annuity (payments at the end of each period) is:
- PMT is the payment each period
- i is the discount rate per period (annual rate ÷ 12 for monthly payments)
- n is the total number of payments
This is the same math used in loan amortisation, which is why a mortgage lender's payment formula is simply this equation rearranged. If payments arrive at the start of each period (an "annuity due", like rent), multiply the result by (1 + i).
Key Takeaway
The higher the discount rate, the less a future payment stream is worth today. The same $3,000 a month is worth far more at a 3% discount rate than at 7%, and the "right" rate is the one thing you have to decide.
The Pension Offer, Worked Out
Here is my uncle's offer: $3,000 a month for 25 years is n = 300 payments. At a 5% annual discount rate, i = 0.05 ÷ 12 = 0.004167.
- (1.004167)−300 = 0.2872
- 1 − 0.2872 = 0.7128
- 0.7128 ÷ 0.004167 = 171.1
- PV = $3,000 × 171.06 = $513,180
So at 5%, the monthly pension is worth about $513,000 today. The $700,000 lump sum is better by roughly $187,000. But change the discount rate and the answer moves:
| Discount rate | Value of $3,000/mo × 25 yrs | Beats $700,000? |
|---|---|---|
| 3% | $632,629 | No |
| 5% | $513,180 | No |
| 7% | $424,461 | No |
Every row says the lump sum wins. That surprised him, so we flipped the question: what rate makes the two offers equal? Solving for it gives about 2.1%. In other words, the pension plan is effectively "paying" him 2.1% a year on his money. If he can reliably earn more than that, the lump sum is the stronger deal on paper.
Two caveats, because "on paper" hides a lot:
- Longevity risk. If he lives to 100, the monthly payments keep coming while a lump sum might run out. The pension is insurance, and insurance has a price.
- Inflation. A fixed $3,000 a month buys noticeably less in year 25. Check what that does with the Inflation Calculator.
⚠️ Note
Many lump-sum offers can be rolled into an IRA tax-free, while taking the cash directly can trigger a large tax bill. In the UK, pension lump sums have their own tax-free allowance rules. Always check the tax treatment before comparing offers.
What Discount Rate Should You Use?
This is the honest hard part. A sensible discount rate reflects what you could realistically earn on the lump sum, with similar safety. A few reference points:
| Benchmark | Typical use as a discount rate |
|---|---|
| Savings account / CD | Low (guaranteed) |
| Government bonds | Medium-low (safe) |
| Balanced portfolio | Higher (not guaranteed) |
The US Internal Revenue Service publishes segment rates for pension lump-sum calculations under Section 417(e) of the tax code, and plans use them to set offers, which is partly why lump sums swing when interest rates move. When rates rise, lump-sum offers shrink; when they fall, they grow.
A practical approach is to run three scenarios, a pessimistic, middle and optimistic rate, and see if the decision flips. If the lump sum wins even at a conservative rate, that's a strong signal. If it only wins at an aggressive rate, you're betting on the market to beat the plan.
The same logic works in other currencies. A UK reader weighing £2,000 a month for 20 years at a 4% discount rate is looking at a present value of about £330,000. An Australian weighing A$4,500 a month for 20 years at 5% gets roughly A$682,000. Plug in your own figures and rate and compare against the cash offer.
The Other Direction: Saving Toward a Stream
Annuity maths runs both ways. If you want to build a pot that can pay out a given stream, you work backwards.
How big a pot funds $3,000 a month? At 5% over 25 years, you'd need about $513,000 on the ordinary-annuity maths above. Pay at the start of each month and it creeps up to about $515,000.
What if you start with $600,000? The same rate and term would support a payment of roughly $3,508 a month.
What does saving look like? A future-value annuity answers "what will regular contributions grow into?" Contributing $500 a month at 7% for 30 years builds about $609,985, even though you only paid in $180,000. The remaining $430,000 is interest, which is why the Compound Interest Calculator and the Retirement Calculator are natural companions.
And for a smaller goal, reaching $100,000 in 10 years at 5% requires saving about $644 a month. You can test your own target with the Savings Calculator.
💡 Pro Tip
When comparing offers, always solve for the implied rate, the discount rate at which both choices are equal. It turns a confusing comparison into one question: can I beat this rate with similar safety?
What did my uncle do? We ran the three scenarios, he talked to an adviser about the rollover rules, and he's still deciding. But he stopped saying "$900,000" and started saying "about 2.1%", and that's progress.
Frequently Asked Questions
What is the difference between present value and future value of an annuity?
Present value is what a stream of future payments is worth today. Future value is what regular contributions will grow into by the end of the term. Present value discounts payments back; future value compounds them forward.
Is an annuity due worth more than an ordinary annuity?
Yes, slightly. Payments arrive one period earlier, so each one has more time to earn interest, or less time to be discounted. The present value is higher by a factor of (1 + i).
Should I take the lump sum or the monthly pension?
It depends on your health, other income, risk tolerance and the tax treatment. The monthly pension gives guaranteed income for life or a fixed term; the lump sum gives flexibility but puts investment and longevity risk on you. Compare the implied rate to what you could realistically earn, and speak to an adviser.
Why do lump-sum offers change when interest rates change?
Plans discount future payments at a rate tied to market interest rates. Higher rates mean future payments are worth less today, so the lump sum shrinks. Lower rates have the opposite effect.
Does this work for lottery winnings or settlements?
Yes. Any fixed series of equal payments can be valued this way. Lottery annuities often pay annually and rise each year, so use the annual frequency and check whether the payments grow.
Try It Yourself
A stream of payments is only comparable to a lump sum once you convert it to today's money, and the discount rate is the lever that decides the outcome. Run your own offer through the Annuity Calculator, switch between present value, future value and required payment, and try three different rates before you decide.
For the bigger picture, see the Retirement Calculator, the Compound Interest Calculator and the Inflation Calculator.
