Present Value of Annuity Calculator
What is a series of future payments worth in today's dollars? This calculator discounts each payment to present value and sums them to show the lump sum equivalent.
Why Future Payments Are Worth Less Today
Imagine someone offers you $1,000 monthly for 10 years—$120,000 total. Should you accept or demand a lump sum instead? The answer depends on what that stream of payments is worth in today's dollars.
Each $1,000 payment is worth less than $1,000 because you have to wait to receive it. The first payment is worth nearly $1,000 (discounted by just one month). The 120th payment is worth much less because it arrives 10 years from now. At a 6% discount rate, that final $1,000 payment is worth only $550 today.
Sum the present value of all 120 payments and you get about $90,000. The $120,000 nominal total is really worth just $90,000 in today's purchasing power. If someone offered you an $85,000 lump sum, you'd be smart to reject it and take the annuity. Offered $95,000? Take the lump sum and invest it yourself.
Real-World Applications
Pension buyouts are the classic case. Your employer offers $150,000 cash to give up a pension worth $1,200 monthly for life. Is it fair? If you expect to live 25 more years, that's $360,000 nominal. But at 5% discount rate, the present value is about $203,000. The $150,000 offer is lowball—you'd lose $53,000 in value by accepting.
Lottery winners face this constantly. 'Win $10 million!' sounds amazing until you read the fine print: $500,000 annually for 20 years. The present value at 4% is about $6.8 million. Take the lump sum option (usually 60% of the advertised amount, or $6 million) and you're getting 88% of the true value. Not bad considering you can invest it immediately at potentially higher returns.
Structured settlement buyers prey on people who don't understand present value. They offer $80,000 cash for a settlement paying $15,000 annually for 10 years. The nominal value is $150,000, so $80,000 sounds like half. But the present value at 6% is only $110,000, making the offer worth 73% of true value. Still a rip-off, just not as bad as it first appears.
Choosing the Right Discount Rate
The discount rate is not arbitrary. It should reflect what you could earn by investing the lump sum at similar risk. Discounting a guaranteed government pension at 10% is wrong because you can't actually earn 10% risk-free. Discounting risky payments at 3% is equally wrong because you're not accounting for the chance of non-payment.
For social security or government pensions, use the treasury rate plus maybe 1%—currently around 4-5%. For corporate pensions, add credit risk: 5-7% depending on the company's financial health. For structured settlements from insurance companies, use 4-6%. For private payments from individuals, use 8-12% to account for default risk.
Higher discount rates make future payments worth less, favoring lump sum options. Lower rates make payment streams more valuable, favoring annuities. This is why buyout offers come when interest rates are high—the present value calculation makes the lump sum look more attractive to workers who don't run the math themselves.
Frequently Asked Questions
What is present value of an annuity?
It's the current lump sum value of a series of future payments, accounting for the time value of money. It tells you how much you'd need to invest today at a given rate to replicate those future payments.
When do I need this calculation?
When evaluating pension buyouts, structured settlements, lottery payouts, or any offer to exchange future payments for an immediate lump sum. It reveals whether the lump sum offer is fair.
What's the formula?
PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is payment amount, r is rate per period, and n is number of periods. This assumes ordinary annuity; multiply by (1 + r) for annuity due.
Should I take a lump sum or annuity payout?
Compare the lump sum offered to the present value you calculate. If the offer exceeds PV at your discount rate, take the lump sum. If not, take the annuity. Also consider taxes, spending discipline, and longevity.
What discount rate should I use?
Use your realistic investment return rate adjusted for risk. For safe income sources like government pensions, use 3-5%. For riskier payments, use 7-10%. Higher rates make future payments worth less today.