Present Value of an Annuity Calculator

Enter payment each period, rate each period, number of payments to find present value. PV = payment × (1 − (1+j)⁻ⁿ)/j, where j is the periodic rate.

INPUT & RESULT

How the result changes

Payment each period (currency units)Current: 500 → 10.6K currency units

Only payment each period changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.

About this calculation

Present Value of an Annuity: find present value from payment each period, rate each period, number of payments. Savings and annuity formulas connect a repeated deposit or payment with a rate and number of periods.

Formula

PV = payment × (1 − (1+j)⁻ⁿ)/j, where j is the periodic rate

Worked example

With Payment each period: 500 currency units, Rate each period: 1 %, Number of payments: 24, present value is 10,621.69 currency units.

Calculation method

The rule is PV = payment × (1 − (1+j)⁻ⁿ)/j, where j is the periodic rate.

For this present value of an annuity example, changing payment each period from 500 currency units to 501 currency units while keeping the other inputs fixed changes present value from 10,621.69 currency units to 10,642.94 currency units.

Reading present value

Future value projects an ending balance; present value expresses future payments in today’s terms; a goal calculation solves for the deposit needed. The formula discounts equal payments made at the end of each period back to the present. The rate is a percentage per payment period, not automatically an annual rate. In the worked values on this page, payment each period 500 currency units, rate each period 1 %, number of payments 24 produce present value 10,621.69 currency units.

Practical use

Use the tool to compare contribution and rate scenarios for a savings target or series of payments. Use it to compare a stream of equal future payments with a lump sum stated today, after choosing a defensible discount rate.

Limits and common mistakes

The rate is assumed constant and deposits occur on the schedule in the formula. Fees, tax, inflation, and changing returns can alter actual outcomes. This is an ordinary annuity. Payments beginning immediately require a different formula; at a zero rate the result is payment times count.

Read the example and units

The worked values on this page use payment each period 500 currency units, rate each period 1 %, and number of payments 24. With those exact entries, the calculator reports present value 10,621.69 currency units. The output describes present value under the displayed equation. It does not automatically include a separate cost, rate, or quantity absent from the listed fields. Keep all money amounts in one currency and check which amount is the base of a percentage. The displayed rule uses only the rate, amount, term, or count you supply; it does not import a market price, account balance, receipt rule, or contract term.

Compare one changed input

For a second scenario, change only payment each period 500 currency units to payment each period 550 currency units and leave the other example entries alone. The result for present value changes from 10,621.69 currency units to 11,683.86 currency units. Comparing one changed input at a time shows exactly which assumption drove the difference in this calculation. This comparison isolates the arithmetic effect of one assumption. Actual fees, contract terms, taxes, behavior, or market outcomes may change a real result, so compare several plausible inputs rather than relying on one precise-looking number.

How to interpret this kind of result

An annuity present-value formula discounts a series of equal payments at the periodic rate entered. The answer values the modeled sequence at the starting point, rather than adding its nominal payments without considering timing. Match the rate period to the payment period: a monthly payment requires a monthly rate if the formula uses monthly steps. For this present value of an annuity calculation, payment each period in currency units, rate each period in %, and number of payments determine present value; the displayed present value 10,621.69 currency units belongs to that exact combination rather than to a different rate, term, or measurement basis.

Scope and practical checks

The model treats payments as equal and regularly spaced. Different payment dates, a changing discount rate, taxes, and credit risk alter the real value of an offered stream. Before comparing two offers, check whether their payment timing and period count match. A present-value result is a mathematical comparison under stated assumptions, not a market quote. Check the payment each period in currency units, rate each period in %, and number of payments entries against the quantities in your own situation before using present value; this page cannot infer a field or condition that you did not enter.

Common questions

What does this present value of an annuity result include?

The present value comes from payment each period in currency units, rate each period in %, and number of payments using the displayed rule PV = payment × (1 − (1+j)⁻ⁿ)/j, where j is the periodic rate. It does not automatically include a condition absent from the listed inputs. Check the applicable account, transaction, or contract terms before using it for a financial decision.