Pension Lump Sum vs Annuity Calculator: The Return You Are Offered
A pension lump sum vs annuity comparison comes down to one question: what return is the pension paying you on the lump sum it replaces? The monthly pension is the lump sum paid back to you with interest, for as long as you live. If that implied return is higher than what you could earn on the lump sum yourself, at similar risk, the annuity is the better deal on the numbers; if it is lower, the lump sum is. In the illustrative example below, a pension of $2,400 a month from age 65 in place of a $400,000 lump sum pays 5.26% a year if you live to 90, 1.03% if you live to 80 and 6.01% if you live to 95. The pension breaks even with the lump sum invested at 5% at age 88.8.
Whether to take the pension lump sum is not something a formula can decide for you. What the formula does is turn two numbers on your election packet into a return and an age, which you can compare with your own expectations.
The formula
The lump sum is a present value. The pension is a stream of monthly payments. They are equal at one interest rate:
lump sum = monthly pension x (1 - (1 + i)^-n) / i
where n is the number of months the pension is paid and i is the monthly
rate. Solve for i, multiply by 12, and you have the implied yearly return.
In a spreadsheet, =RATE(n, pension, -lump)*12 does it.
Two things to notice. First, n depends on how long you live, so there is no single answer: there is one return for each age at death. Second, the payout rate is not the return. $2,400 a month is $28,800 a year, which is 7.2% of $400,000. That 7.2% includes the lump sum itself being handed back, so the real return is always lower.
Worked example: the implied return
These figures are illustrative, not an offer anyone received. The lump sum is $400,000, the single-life pension is $2,400 a month starting at 65, and payments are level with no cost-of-living increase.
| Pension paid until age | Months paid | Total paid | Implied yearly return |
|---|---|---|---|
| 75 | 120 | $288,000 | -6.18% |
| 80 | 180 | $432,000 | 1.03% |
| 85 | 240 | $576,000 | 3.89% |
| 90 | 300 | $720,000 | 5.26% |
| 95 | 360 | $864,000 | 6.01% |
Paid to 90, the pension pays out $720,000 in total, but spread over time that is a 5.26% return. Paid to 95, it is 6.01%, still under the 7.2% payout rate. If the pension stops at 75, the return is negative: -6.18%. The longer you live, the better the pension did.
So the comparison is: would you, with $400,000 in hand, earn more than 5.26% a year after fees for the rest of your life, with the risk of markets along the way? The pension’s return has no market risk and no chance of running out; the lump sum’s return is whatever you manage, and whatever is left goes to your heirs.
The break-even age
The same numbers as a break-even age. Ignoring interest, $2,400 a month repays $400,000 in 13.9 years, by age 78.9. That is the plain count, and it flatters the pension, because the lump sum would be invested.
If the lump sum earns 5% a year and you take $2,400 a month out of it, it lasts until age 88.8, 9.9 years later than the plain count. At 80 there would still be $203,988 left. Past 88.8, the lump sum is gone and the pension is still paying. That is the break-even seen from both sides: live past 88.8 and the pension paid more; die before it and the lump sum did, with the remainder going to heirs.
To make the money last exactly to 90 at 5%, you could take $2,338.36 a month, $61.64 less than the pension.
The insight: interest rates set the offer
Run the present value the other way: what is $2,400 a month to 90 worth today, at different discount rates?
| Discount rate | Pension’s value today, paid to 90 | Against the lump sum |
|---|---|---|
| 4% | $454,686 | +$54,686 |
| 5% | $410,544 | +$10,544 |
| 6% | $372,496 | -$27,504 |
| 7% | $339,569 | -$60,431 |
At 5% the pension is worth $410,544, $10,544 more than the lump sum offered. At 6% it is worth $372,496, less than the lump sum. The crossover sits at 5.26%, the implied return from the first table - the same number, found from the other direction.
Two things follow. One: the discount rate you choose decides the answer, so choose it honestly - what you could earn on the lump sum at similar risk, not the best year you remember. Two: plans compute lump sums from interest rates, so a rise from 5% to 6% cuts the value of the same pension from $410,544 to $372,496, $38,048 or 9.3%. If your benefit date is close to a point where your plan resets its rates, the offer can change for the same pension. Your plan uses its own rates and a mortality table, not a single end age, so its figure will differ from this one; the direction is the same.
Things that move the answer
- Cost-of-living increases. A pension that rises each year is worth more than the same starting amount held flat. The pack compares a COLA pension against a higher flat one.
- A survivor option. Illustrative: taking $2,100 a month with a full survivor benefit instead of $2,400 single-life costs $300 a month, $72,000 if you live to 85. If your spouse then lives 7 more years, they collect $176,400; they need 2.9 years to recover the cost. It is insurance: it pays only if you die first.
- Tax. Both choices are taxed, and how depends on rollover choices this post does not model.
- Other income. A pension that covers fixed bills frees the rest of your savings to take risk. The Coast FIRE calculator and the compound interest calculator show how a balance grows when you leave it alone.
How these were calculated
Payments are level, monthly, at the end of each month, from the starting age to the age shown. The implied return is the monthly rate at which those payments are worth the lump sum, times 12, found by iteration and checked by discounting every payment back one month at a time. The break-even age is the month a lump sum earning the return, paying the pension’s amount at each month end, runs out. Present values discount each month’s payment at the yearly rate divided by 12. The survivor figures are plain totals, not discounted. No tax, no inflation, no mortality table.
Every figure on this page was computed twice - once by the code behind the calculator pack below, once by a separate month-by-month implementation - and the two agree to the cent. The lump sum, pension, ages and rates are illustrative inputs, not an offer, a market rate or a forecast. None of this is financial, legal or tax advice; your plan’s election packet and a qualified professional are the authorities for your own decision.
If you want to run this on the numbers in your own election packet - the implied return, the break-even age, the present value, a COLA pension, the survivor option and how long the lump sum lasts - the pack below does it in linked spreadsheets with every formula visible.