Present Value of Annuity Calculator

The present value of an annuity answers a lump-sum question: what is a fixed stream of future payments worth today? Instead of projecting deposits forward, this calculator walks each payment backward to the present using the selected discount rate. That makes it useful for comparing a promised payment stream with a cash offer, analyzing lease-like payments, checking installment settlement terms, or learning how time-value-of-money math treats equal cash flows.

This page is deliberately different from the future value of annuity calculator. Future value asks what equal payments grow into at the end of the schedule. Present value asks what those future payments are worth now. For a broader page that can combine an opening balance with deposits or withdrawals, use the annuity calculator. For a lump sum that must support income, use the annuity payout calculator. For never-ending payments, compare the finite result with the perpetuity calculator.

How the calculator matches the form

The form asks for a payment amount, interest rate, number of periods, payment timing, and compounding frequency. The calculator accepts the payment and rate as numbers, treats the number of periods as an integer, and rejects a period count that is not a positive whole number. It then maps the compounding choice to 1, 2, 4, or 12 periods per year.

The effective rate used in the schedule is:

$\text{effective rate} = \frac{\text{annual rate}}{100 \times \text{compounding periods}}$

Then the calculator loops through every payment period. For ordinary annuity timing, period 1 is discounted for one period, period 2 for two periods, and so on. For annuity due timing, period 1 is discounted for zero periods because it is assumed to occur immediately at the beginning of the first period. The displayed present value is the sum of those discounted payments.

Formula

For an ordinary annuity with equal payment PMT, periodic discount rate r, and number of payments n, the closed-form formula is:

$\text{PV ordinary} = \text{PMT} \times \frac{1 - (1+r)^{-n}}{r}$

For an annuity due, each payment happens one period earlier. The ordinary result is multiplied by one extra timing factor:

$\text{PV due} = \text{PV ordinary} \times (1+r)$

The calculator’s displayed schedule uses the equivalent period-by-period form:

$\text{period PV} = \text{PMT} \times (1+r)^{-\text{time value}}$

For ordinary timing, the time value is the period number. For beginning timing, the time value is one less than the period number.

Worked example matching the default inputs

The default inputs are a $1,000 payment, 5% interest, 10 periods, end-of-period timing, and annual compounding. Annual compounding means the effective rate is 0.05. The first payment is discounted by one year, so its present value is $1,000 divided by 1.05, or about $952.38. The tenth payment is discounted by ten years, so it contributes about $613.91.

Adding all ten discounted payments produces $7,721.73. The total undiscounted payments are $10,000, so the gap of $2,278.27 is the time-value adjustment created by the 5% discount rate. The result panel also reports the effective rate as 5.00% and the payment timing as End.

If the same inputs are switched to beginning-of-period timing, the first $1,000 payment is not discounted at all because it occurs at time zero. Each later payment is also discounted for one fewer period. The sum becomes $8,107.82, which is exactly the ordinary result multiplied by 1.05.

Present value versus a product quote

This calculator values a mathematical cash-flow stream. It does not tell you what an insurance company should charge for an income annuity, nor does it value a pension with survivor benefits or inflation adjustments. Insurance annuities may depend on life expectancy, gender-neutral or state-specific rules, insurer expenses, guarantees, surrender charges, riders, and interest-crediting formulas. Pension choices can depend on mortality tables and plan rules.

Use the result to compare clear alternatives. If someone offers ten annual payments of $1,000 or a lump sum of $7,500, the default present value of $7,721.73 suggests the payments are worth slightly more than the lump sum under a 5% discount assumption. At a higher discount rate, the same stream would be worth less; at a lower rate, it would be worth more.

Ordinary versus due timing

Timing is not a formatting choice; it changes the math. Ordinary annuities place payments at period end. Common examples include many bond coupons, installment loan payments, and retirement withdrawals taken after a month or year has passed. Annuities due place payments at period beginning. Rent, lease payments, and subscription charges often behave this way.

Because present value rewards earlier cash, annuity due produces a higher value when the rate is positive. The difference is one period of return. With a monthly rate, that difference may look small for a single payment, but over a long stream it can change a lump-sum comparison by hundreds or thousands of dollars.

Tips for accurate inputs

• Use the discount rate that reflects the comparison you are making. A risk-free Treasury rate, a personal required return, and an investment hurdle rate can lead to different present values.
• Keep periods and compounding aligned. If you enter monthly payments as periods, monthly compounding often matches better than annual compounding.
• Do not mix nominal and effective rates without understanding the difference. This calculator divides the nominal annual rate by the selected compounding count.
• Use a separate scenario for taxes, fees, or inflation. The form does not automatically reduce payments for tax withholding or raise them for cost-of-living adjustments.
• Review the schedule when a result looks surprising. It shows which payments contribute most to the present value.

Informational note

Present value is a decision aid, not a recommendation. It can help you compare a lump sum and a fixed payment stream, but it cannot judge credit risk, liquidity needs, taxes, contractual guarantees, or whether a financial product is suitable for you.

Formula sources and scope

• Compound Interest Calculator — U.S. Securities and Exchange Commission, Investor.gov; live federal investor tool accessed 2026-07-09; United States; arithmetic is general. Supports: ordinary PV=PMT×(1-(1+r)^(-n))/r; annuity-due PV=ordinaryPV×(1+r); straight-line PMT×n when r=0. Accessed 2026-07-09.
• Principles of Finance — OpenStax, Rice University (peer-reviewed open textbook); 2022 first edition, ISBN 978-1-951693-54-1; Jurisdiction-neutral finance definitions. Supports: ordinary PV=PMT×(1-(1+r)^(-n))/r; annuity-due PV=ordinaryPV×(1+r); straight-line PMT×n when r=0. Accessed 2026-07-09.

These sources support the stated formula or definition. Results remain estimates based on the entered values and do not replace financial, legal, tax, lending, or investment advice. Compare periods, units, accounting definitions, and jurisdiction-specific rules before acting.

Sources

• SEC Investor.gov, Annuities — overview of annuity contracts, types, income streams, and investor considerations.
• FINRA, Annuities — investor education overview of annuity products and risks.