Lump Sum vs Annuity Calculator
Pension and lottery winners are often handed a choice: take one large lump sum now, or accept an annuity that pays a fixed amount every year for decades. The two are not directly comparable because a dollar received years from now is worth less than a dollar in hand today. This calculator settles the comparison by discounting every annuity payment back to its present value at a rate you choose, summing them, and then putting that figure side by side with the cash offer so you can see which option is genuinely worth more in today money.
Formula
PV = PMT × (1 − (1 + r)^(−n)) / r
- PV
- Present value of the annuity stream, compared against the lump sum
- PMT
- Annual payment the annuity pays each year
- r
- Discount rate per year as a decimal (rate% divided by 100)
- n
- Number of years the annuity is paid
How it works
- Enter the lump sum on offer, the annual payment the annuity would pay, the number of years it runs, and a discount rate that reflects what you could realistically earn on invested money or your required return.
- The tool discounts the stream of equal annual payments to a single present value using the ordinary annuity formula, treating each payment as arriving at the end of its year.
- It compares that present value to the lump sum and reports the difference. If the discounted annuity is worth more, the annuity wins; otherwise the lump sum is the better deal. A higher discount rate shrinks the annuity present value and tilts the decision toward the lump sum.
Worked example
A pension offers either a $500,000 lump sum today or $35,000 per year for 25 years. You expect a 3% return on safe investments.
- Convert the rate: r = 3 divided by 100 = 0.03; payments n = 25; PMT = 35,000.
- Apply the annuity formula: PV = 35,000 × (1 − 1.03^(−25)) ÷ 0.03.
- The annuity factor is about 17.4131, so PV = 35,000 × 17.4131 = $609,460.17.
- Compare to the lump sum: 609,460.17 − 500,000 = $109,460.17 in favor of the annuity.
At a 3% discount rate the annuity is worth about $609,460.17 today, roughly $109,460.17 more than the $500,000 lump sum, so the annuity is the better choice. Raise the discount rate to 10% and that present value falls to $317,696.40, which flips the decision toward the lump sum.
Frequently asked questions
- What discount rate should I use?
- Use a rate close to what you could realistically and safely earn if you invested the lump sum yourself, or your required rate of return. Conservative savers often use 3% to 5%, while someone confident in higher market returns might use 7% or more. The rate is the single most important assumption, so it helps to test a range.
- Why does a higher discount rate favor the lump sum?
- A higher discount rate means you assume you can earn more on money you hold today, so future payments are discounted more heavily and are worth less in present terms. As the rate rises, the present value of the annuity stream shrinks while the lump sum stays fixed, so at some crossover rate the lump sum becomes the better deal.
- What does this calculation ignore?
- This is a pure present-value comparison and does not account for taxes, inflation eroding fixed payments, longevity risk if you outlive the term, the credit risk of the payer, or the behavioral risk of spending a lump sum too quickly. Treat the result as a starting point and weigh those factors before deciding.