Present Value of Annuity Calculator
Find the lump sum today that is equivalent to a future stream of equal payments. Enter the payment amount, interest rate, number of periods, compounding frequency, and payment timing to get the present value instantly. This calculator covers ordinary annuities, annuities due, growing annuities, and perpetuities, and shows the full step-by-step working so you can see exactly where every number comes from.
What is the present value of an annuity?
An annuity is a series of equal, regularly spaced cash flows. The present value of that series is the single lump sum today that is economically equivalent to all those future payments, given a specific interest (discount) rate. It answers a practical question: if someone offers you $1,000 a year for 20 years, what is that promise worth in today's money? The further in the future a payment falls, and the higher the discount rate, the less it is worth today. Present value is the foundation of loan pricing, bond valuation, retirement planning, and court-settlement calculations.
Ordinary annuity vs. annuity due
The timing of the first payment matters. An ordinary (or immediate) annuity pays at the end of each period, which is how most loans and bonds work. An annuity due pays at the beginning of each period, which is how most leases and insurance premiums are structured. An annuity due is always worth slightly more than an equivalent ordinary annuity, because each payment is received one period earlier. The formula for an annuity due is simply the ordinary-annuity formula multiplied by (1 + r), where r is the periodic interest rate.
Growing annuities and perpetuities
A growing annuity pays an amount that increases at a constant rate g each period. If that growth continues forever, it becomes a growing perpetuity. A regular perpetuity pays a fixed amount forever, and its present value collapses to the simple fraction PMT / r. A growing perpetuity adds inflation-matching payments, with a present value of PMT / (r - g), which only has a finite answer when the discount rate exceeds the growth rate. These structures appear in dividend discount models, endowments, and long-run retirement income analysis.
The role of compounding and payment frequency
When the compounding frequency differs from the payment frequency, you need to convert the nominal annual rate to an equivalent effective rate per payment period before applying any formula. For example, a 6% rate compounded monthly with quarterly payments requires a quarterly rate of (1 + 0.06/12)^3 - 1 = 1.5075%, not the simpler 1.5% you would get by dividing 6% by 4. This calculator handles all combinations automatically, including continuous compounding, and shows the derived effective-per-period rate in the results so you can verify the math.
Quick-reference: PV of $1,000/year ordinary annuity at common rates
| Duration | 3% | 5% | 7% | 10% |
|---|---|---|---|---|
| 5 years | $4,580 | $4,329 | $4,100 | $3,791 |
| 10 years | $8,530 | $7,722 | $7,024 | $6,145 |
| 20 years | $14,877 | $12,462 | $10,594 | $8,514 |
| 30 years | $19,600 | $15,372 | $12,409 | $9,427 |
Present value in USD of an annual payment of $1,000, discounted at various rates and durations. Useful for sanity-checking your result.
Frequently asked questions
What is the present value of an annuity formula?
For an ordinary annuity, PV = PMT x [(1 - (1 + r)^-n) / r], where PMT is the payment per period, r is the effective interest rate per period, and n is the number of periods. When r equals zero, PV simplifies to PMT x n. For an annuity due, multiply that result by (1 + r). For a growing annuity with growth rate g, PV = PMT x [1 - ((1+g)/(1+r))^n] / (r - g). Perpetuity PV is simply PMT / r.
What is the difference between ordinary annuity and annuity due?
The only difference is payment timing. An ordinary annuity pays at the end of each period: mortgages, most bonds and loan repayments follow this pattern. An annuity due pays at the beginning of each period: apartment leases and insurance premiums are typical examples. Because an annuity due receives each payment one period earlier, its present value is always higher than an equivalent ordinary annuity by a factor of (1 + r).
What discount rate should I use?
The discount rate represents the opportunity cost of money or the required rate of return. For personal finance, you might use a savings-account rate, a mortgage rate, or an expected investment return. For corporate finance, analysts often use the weighted average cost of capital (WACC). For court settlements and insurance, actuarial or risk-free rates are common. There is no universally correct rate; it depends on the risk and the alternative uses of the capital.
Why does a higher interest rate give a lower present value?
A higher discount rate penalizes distant cash flows more heavily. Think of it this way: if you could earn 10% per year safely elsewhere, a payment arriving in 10 years is worth only about 39 cents on today's dollar. At 2%, it is still worth about 82 cents. The higher the return available elsewhere, the less you need in the bank today to match those future payments, so the present value falls.
What is a growing annuity?
A growing annuity is a series of payments that increases at a constant rate g each period. For example, retirement withdrawals that rise by 2% annually to keep pace with inflation form a growing annuity. Its present value formula is PMT x [1 - ((1+g)/(1+r))^n] / (r - g). If g equals r, the formula simplifies to PMT x n / (1 + r). Growing perpetuities follow the Gordon Growth Model: PV = PMT / (r - g), valid only when r exceeds g.
What is the difference between present value and future value of an annuity?
Present value tells you what a series of future payments is worth right now. Future value tells you how much that same series would accumulate to at the end of the term if each payment were reinvested at the same rate. They are related: FV = PV x (1 + r)^n. Use present value when deciding how much to pay for a stream of income today, and future value when projecting how much a savings plan will grow to.