This calculator calculates the present value of an ordinary annuity, where payments occur at the end of each period.
How to Calculate the Present Value of an Annuity
The present value of an annuity shows what a series of equal future payments is worth today, based on a specified interest rate and number of payment periods.
The present value of an ordinary annuity can be calculated using the following formula:
PV = PMT × [1 − (1 + i)⁻ⁿ] / i
where:
PV = present value of the annuity
PMT = periodic payment amount
i = interest rate per period
n = number of periods
Present Value of an Annuity Example
Suppose you expect to receive $1,000 per year for 5 years and the interest rate is 5% per year.
Using the present value of an annuity formula:
PV = $1,000 × [1 − (1 + 0.05)⁻⁵] / 0.05
The present value is approximately $4,329.48.
This means that receiving $1,000 at the end of each year for five years is worth approximately $4,329.48 today when discounted at a 5% annual rate.
What Is an Annuity?
An annuity is a series of equal payments made or received at regular intervals. Payments may occur monthly, quarterly, annually, or at another regular interval.
Examples can include loan payments, retirement payments, and certain investment cash flows.
Present Value of an Ordinary Annuity vs. Annuity Due
An ordinary annuity assumes that payments are made at the end of each period.
An annuity due assumes that payments are made at the beginning of each period.
This calculator calculates the present value of an ordinary annuity, where payments occur at the end of each period.
Why Calculate the Present Value of an Annuity?
Calculating present value makes it possible to compare future payments with an amount of money today. Because money received in the future is generally worth less than the same amount received today, future payments are discounted using an appropriate interest rate.
Present value calculations are commonly used in finance, accounting, investment analysis, and loan calculations.
Frequently Asked Questions
What happens when the interest rate increases?
With all other factors remaining the same, a higher discount rate results in a lower present value of the annuity.
Does the interest rate have to match the payment period?
Yes. The interest rate and the payment period should use the same time interval. For example, if payments are monthly, the calculation should use a monthly interest rate and the number of monthly periods.
Does this calculator calculate an annuity due?
No. This calculator is designed for an ordinary annuity, where payments are assumed to occur at the end of each period.
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