Present Value of Annuity Calculator
Find out what a series of equal future payments is worth in today's dollars. Use it to value pension streams, lease obligations, lottery payouts, or any fixed cash-flow schedule before making a financial commitment.
About this calculator
The present value of an annuity (PV) tells you the lump-sum equivalent today of receiving equal payments over multiple periods, discounted at a given rate. For an ordinary annuity (payments at period end): PV = payment × ((1 − (1 + r)^(−n)) / r). For an annuity-due (payments at period start), each payment arrives one period earlier, so the result is multiplied by (1 + r): PV_due = payment × ((1 − (1 + r)^(−n)) / r) × (1 + r). Here r is the periodic discount rate (annual rate ÷ 100) and n is the number of periods. A higher discount rate reduces PV because distant money is worth less when the opportunity cost of capital is high. This concept is central to bond pricing, lease accounting (IFRS 16/ASC 842), and retirement planning.
How to use
Scenario: you will receive $1,000 per month for 5 years (60 periods) from a structured settlement. The discount rate is 6% per year (0.5% per month). Using an ordinary annuity: PV = $1,000 × ((1 − (1.005)^(−60)) / 0.005) = $1,000 × ((1 − 0.7414) / 0.005) = $1,000 × (0.2586 / 0.005) = $1,000 × 51.73 = $51,726. This means accepting a lump sum of $51,726 today is financially equivalent to receiving those 60 monthly payments at a 6% discount rate. If payments were due at the start of each month (annuity-due), multiply by 1.005 to get $51,984.
Frequently asked questions
What is the difference between an ordinary annuity and an annuity-due in present value calculations?
An ordinary annuity assumes each payment arrives at the end of the period, while an annuity-due assumes payment at the beginning. Because annuity-due payments arrive one period sooner, each payment has less discounting applied, making the present value higher by a factor of (1 + r). In practical terms, rent paid at the start of the month follows an annuity-due pattern, while bond coupon payments received at the end of the period follow the ordinary annuity pattern. Always confirm payment timing before using the result for negotiation or accounting purposes.
How does the discount rate affect the present value of an annuity?
The discount rate represents the opportunity cost of money — what you could earn by investing the funds elsewhere. A higher discount rate shrinks each future payment's present value, because you are penalizing the wait more heavily. For example, $1,000 per year for 10 years is worth about $7,722 at a 5% rate but only $6,710 at an 8% rate. This sensitivity means small changes in the assumed rate can significantly alter a valuation, especially for long-duration annuities.
When should I use present value of annuity instead of a future value calculation?
Use present value when you need to answer 'how much is this future income stream worth right now?' — for example, when comparing a lump-sum settlement offer against monthly payments, valuing a business acquisition, or recording a lease liability on a balance sheet. Future value calculations answer the reverse question: how much will my current savings grow to over time? If you're on the receiving end of a stream of payments and need to make a decision today, present value is the correct tool.