Compare a pension lump-sum offer with monthly lifetime payments or calculate an equivalent lump sum using COLA, longevity, and discount assumptions.
Pension Lump Sum vs Monthly Payment Formula
The monthly pension is converted to an estimated lump-sum value by discounting its future payments.
For a growing pension:
PV=P*(1-((1+g)/(1+r))^n)/(r-g)
Nominal lifetime payments are:
Total=P*((1+g)^n-1)/g
Variables:
- P is the first annual pension payment
- g is annual COLA
- r is the discount or investment rate
- n is payment years
Comparison mode measures the pension's present value against an actual offer. Equivalent-lump mode returns the present value itself.
A higher discount rate lowers the value assigned to distant payments.
Test several planning ages because longevity is a major driver of value.
Effect of Assumptions on Pension Value
Longer payment periods and larger COLAs increase value; higher discount rates reduce it.
| Monthly pension | Years | COLA | Discount rate | Illustrative value |
|---|---|---|---|---|
| $3,500 | 25 | 0% | 3% | About $731,000 |
| $3,500 | 25 | 0% | 5% | About $592,000 |
| $3,500 | 25 | 2% | 5% | About $739,000 |
| $3,500 | 30 | 2% | 5% | About $820,000 |
Example Problems
Example 1: Compare an offer.
Compare a $650,000 offer with $3,500 per month from age 65 through 90, a 2 percent COLA, and a 5 percent discount rate.
Example 2: Find an equivalent lump sum.
Leave the offer out and calculate the present value of the same payment stream.
Frequently Asked Questions
What discount rate should I use?
Use a rate consistent with the risk and investment alternative, and test a range rather than one optimistic number.
Does higher present value settle the decision?
No. A pension provides longevity protection, while a lump sum offers flexibility and inheritance potential.
How are survivor benefits handled?
This calculator models one payment stream. Use a survivor-benefit calculator for joint elections.
