How the lump sum vs annuity math works
How is a pension lump sum calculated?
Short answer: your lump sum is the present value of your accrued monthly pension, computed with interest rates and mortality tables set by federal law. It is a legal minimum, not a negotiated deal.
Under Internal Revenue Code section 417(e)(3), a pension plan must compute a lump sum as the present value of the annuity you earned, using IRS-published segment interest rates and a standard mortality table. In plain terms: the plan discounts every future monthly payment back to today and adds them up.
where P = monthly benefit, r = monthly interest rate, n = months of life expectancy
Because of that formula, lump sums move opposite to interest rates: when rates fall, the lump sum rises; when rates rise, the lump sum shrinks. If your offer looks smaller than last year's, rising rates are usually the reason.
What is the break-even age?
Short answer: the break-even age is the age at which the present value of the annuity payments you have collected so far catches up to the lump sum. Live past it and the annuity was the better deal.
Set the present-value formula equal to the lump sum (L) and solve for the number of months (n):
(1 + r)−n = 1 − L·r / P
n = −ln(1 − L·r / P) / ln(1 + r)
Divide n by 12 and add your current age to get the break-even age. One edge case matters: if L·r/P ≥ 1, the answer is never. That means the monthly interest the lump sum could earn is bigger than the monthly pension payment, so the annuity never catches up at that discount rate.
How does a joint-and-survivor benefit change the answer?
Short answer: electing a survivor benefit reduces your monthly check while you are alive, then pays your spouse the elected percentage after you die. The annuity usually looks better for couples than for single retirees.
A 100% joint-and-survivor annuity typically pays about 84% to 88% of the single-life monthly benefit; a 50% option pays roughly 91% to 93%. The exact reduction comes from your plan's actuarial tables and depends on both spouses' ages. The calculator below uses editable estimates and extends the payment stream for the survivor's extra years, discounted at the same rate.
What discount rate should I use?
Short answer: use the annual after-tax return you realistically expect to earn if you invest the lump sum. The default here is 5%, a conservative long-term assumption.
The discount rate is the hinge of the whole comparison. A higher rate favors the lump sum (future payments are worth less today); a lower rate favors the annuity. If you would invest conservatively, use 3% to 4%. A balanced portfolio might justify 5% to 6%. Whatever you pick, try a point or two in each direction to see how sensitive your answer is. The calculator also reports the implied rate: the return you would need to earn on the lump sum to exactly match the annuity.
How are lump sums taxed?
Short answer: a lump sum is taxed as ordinary income in the year you receive it, unless you roll it directly into an IRA or 401(k), which defers the tax. Annuity payments are taxed as ordinary income each year as they arrive.
Taking the lump sum in cash in a single year can push you into a higher tax bracket, which is one of the strongest practical arguments for the direct rollover. The calculator shows after-tax totals using your marginal bracket so you can compare both options on equal footing.
Run your numbers
Survivor options compare the joint-and-survivor annuity to the lump sum. "Single life" compares the full monthly amount above.
Advanced assumptions (editable)
Reduction factors are typical-plan estimates for same-age spouses. Your plan's exact factor comes from its benefit statement.
Guides
The 6% Rule: A Quick Screen for Lump Sum vs. Annuity
One division that tells you which side of the fence you are on, with worked examples and caveats.
Rolling a Pension Lump Sum Into an IRA Without a Tax Mess
Direct vs. indirect rollovers, the 20% withholding trap, and the 60-day rule.
Frequently Asked Questions
What is the break-even age for a pension lump sum?
The break-even age is the age at which the present value of the annuity payments you have collected catches up to the lump sum you were offered. It comes from solving the annuity present-value formula for the number of months: n = −ln(1 − L·r/P) / ln(1+r), then adding n/12 to your current age. If the lump sum's monthly earnings at your discount rate exceed the monthly pension payment, the answer is "never" and the annuity never catches up mathematically.
How is a pension lump sum calculated?
By federal law (IRC 417(e)(3)), the lump sum is the present value of your accrued monthly benefit, computed with IRS-published segment interest rates and a standard mortality table. The formula is: lump sum = P × [1 − (1+r)−n] / r. When interest rates fall, lump sums rise; when rates rise, lump sums shrink. The law also sets a floor: your plan cannot pay less than this present value.
How much does a joint-and-survivor benefit reduce my pension?
A 100% joint-and-survivor annuity typically pays about 84% to 88% of the single-life benefit, a 75% option about 88% to 91%, and a 50% option about 91% to 93%. The exact reduction is set by your plan's actuarial tables and depends on both spouses' ages, so check your benefit statement. The calculator above uses editable estimates for these factors.
How are taxes on a pension lump sum treated?
A lump sum taken in cash is taxed as ordinary income in the year you receive it, which can push you into a higher bracket. A direct rollover into a traditional IRA or 401(k) defers the tax until you withdraw. Annuity payments are taxed as ordinary income each year as they arrive. Because the two options are taxed so differently in time, always compare them after tax, as this calculator does.
What discount rate should I use in the comparison?
Use the after-tax annual return you realistically expect to earn if you invest the lump sum. A conservative investor might use 3% to 4%; a balanced portfolio might justify 5% to 6%. The rate is the hinge of the decision: higher rates favor the lump sum, lower rates favor the annuity. Also look at the implied rate the calculator reports, which is the return you would need to earn on the lump sum to exactly match the annuity.
Should I take the lump sum or the annuity?
There is no universal answer. The annuity usually wins if you expect a long life, value a guaranteed check, or would invest the lump sum conservatively. The lump sum usually wins if you are in poor health, can earn a higher return, want control of the money, or worry about your employer's plan. Run both scenarios above, check the break-even age against your family longevity, and talk to a fiduciary advisor before deciding. This tool is for estimates only and is not financial advice.
This calculator is free to use. We may earn a commission if you connect with a financial advisor or use an annuity marketplace through links on this page. These relationships never change the math: every number on this page is computed live from the values you enter using standard present-value formulas.