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Present Value of Annuity Calculator

Calculate the present value of a series of equal future payments.

The Present Value of Annuity Calculator is a free financial calculator. Calculate the present value of a series of equal future payments. Plan your finances accurately and make better economic decisions.
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What Is the Present Value of an Annuity?

The present value of an annuity tells you what a series of equal future payments is worth in today's money. Because a dollar received tomorrow is worth less than a dollar in hand today — due to inflation and the opportunity cost of capital — you need to "discount" future cash flows back to the present. This calculator does exactly that: give it a regular payment amount, an interest rate, and a number of periods, and it returns the lump-sum equivalent right now.

This matters in real decisions. If someone offers you $500 a month for 10 years, or $45,000 today, which is better? At a 5% annual rate, the annuity stream is worth $46,587 today — so the lump sum is the worse deal. At 8%, the present value drops to $40,965, making the lump sum more attractive. The rate you choose changes everything.

The Formula

PV = PMT × [1 − (1 + r)⁻ⁿ] ÷ r

  • PV — Present value (the answer: what the stream is worth today)
  • PMT — Periodic payment (each instalment, same amount every period)
  • r — Interest rate per period (annual rate ÷ 12 for monthly payments)
  • n — Total number of payment periods

Worked Example

Pension Buyout Decision

Your employer offers you either $1,200/month for 20 years, or a one-time lump sum of $160,000 today. The discount rate is 6% annually (0.5% per month). Which is worth more?

Step 1 — Convert rate: 6% annual ÷ 12 = 0.5% per month = 0.005

Step 2 — Count periods: 20 years × 12 months = 240 periods

Step 3 — Apply formula: PV = 1,200 × [1 − (1.005)⁻²⁴⁰] ÷ 0.005

Step 4 — Solve: (1.005)⁻²⁴⁰ = 0.3021, so [1 − 0.3021] ÷ 0.005 = 139.58. PV = 1,200 × 139.58 = $167,497

Conclusion: The pension stream is worth $167,497 today — more than the $160,000 lump sum. Take the pension.

Common Uses

  • Pension and retirement planning: Comparing lump-sum buyouts against monthly pension income
  • Lottery prizes: Deciding between annuity payments and a discounted cash payout option
  • Lease valuation: Calculating what a series of lease payments is worth as an upfront cost
  • Bond pricing: Valuing the coupon payment stream of a fixed-income security
  • Structured settlements: Evaluating legal or insurance settlement payment streams

Common Mistakes

  • Using the annual rate with monthly payments: If payments are monthly, divide the annual rate by 12. Using 6% instead of 0.5% per month will massively understate the present value.
  • Confusing ordinary annuity and annuity-due: This calculator assumes payments arrive at the end of each period. If payments arrive at the beginning (like rent paid in advance), multiply the result by (1 + r).
  • Choosing the wrong discount rate: The rate should reflect the risk of the payments and your alternative investment return — not just a savings account rate. Riskier income streams deserve a higher discount rate, which lowers present value.

Pro Tip

When evaluating a pension buyout or structured settlement, use the yield on an AA-rated corporate bond of similar duration as your discount rate. It reflects your true opportunity cost better than a savings rate, and it's the standard actuaries use when valuing pension liabilities.

Frequently Asked Questions

Present value tells you what future payments are worth today. Future value tells you what regular contributions will grow to by a future date. Use present value when choosing between a payment stream and a lump sum now. Use future value when projecting how much a savings plan will accumulate.

Match the rate to the period. For monthly payments: divide the annual rate by 12 and multiply years by 12. For quarterly: divide by 4 and multiply years by 4. Always keep rate and number of periods in the same unit.

It depends on risk. For guaranteed government payments, use a Treasury yield. For corporate pensions, use an AA bond yield. For personal decisions like lottery payouts, many financial planners use 4–6% to represent a balanced portfolio's expected real return.

For a never-ending payment stream, the formula simplifies to PV = PMT ÷ r. A payment of $1,000/year forever at 5% is worth $1,000 ÷ 0.05 = $20,000 today. This applies to preferred stock dividends and some endowment distributions.

Written and reviewed by the CalcToWork editorial team. Last updated: 2026-04-29.

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Frequently Asked Questions

Present value tells you what future payments are worth today. Future value tells you what regular contributions will grow to by a future date. Use present value when choosing between a payment stream and a lump sum now. Use future value when projecting how much a savings plan will accumulate.
Match the rate to the period. For monthly payments: divide the annual rate by 12 and multiply years by 12. For quarterly: divide by 4 and multiply years by 4. Always keep rate and number of periods in the same unit.
It depends on risk. For guaranteed government payments, use a Treasury yield. For corporate pensions, use an AA bond yield. For personal decisions like lottery payouts, many financial planners use 4–6% to represent a balanced portfolio's expected real return.
For a never-ending payment stream, the formula simplifies to PV = PMT ÷ r. A payment of $1,000/year forever at 5% is worth $1,000 ÷ 0.05 = $20,000 today. This applies to preferred stock dividends and some endowment distributions.