What Is the Present Value of an Annuity?

An annuity is a series of equal payments made at regular intervals, such as $1,200 every year for 10 years. The present value of an annuity is what all of those future payments are worth today, as a single amount.

Money you receive later is worth less than money you have now, because money you have now could be invested and earn a return. So each future payment is discounted back to today, and the further away it is, the less it is worth. The rate used for this is the discount rate: the return you could earn elsewhere, such as on a savings account, a bond or an investment of similar risk.

Common uses:

Lump sum or payments? Comparing a lottery prize, pension or settlement paid over time with a single payment today.
Structured settlements: what a stream of future payments is worth if you sell it for cash now.
Loans: a loan's amount is the present value of its payments at the loan's interest rate.
Retirement planning: how much you need saved today to pay yourself a set income for a number of years.

Types of annuities by payment timing

Ordinary annuity: payments come at the end of each period, like most loan payments and bond interest.
Annuity due: payments come at the beginning of each period, like rent and lease payments. Each payment arrives one period sooner, so the present value is higher.

How to Calculate the Present Value of an Annuity

Ordinary annuity (payments at the end)

PV = PMT \times \frac{1 - {(1 + \frac{i}{m})}^{- n \cdot m}}{\frac{i}{m}}

Annuity due (payments at the beginning)

{PV}_{due} = {PV}_{ordinary} \times (1 + \frac{i}{m})

Where:

PMT: the payment made each period.
i: the yearly discount rate as a decimal (6% = 0.06).
m: the number of payments a year: 1 annually, 2 semi-annually, 4 quarterly, 12 monthly, 365 daily.
n: the number of years, so n × m is the number of payments.

The formula adds up every payment divided by (1 + i/m) raised to the number of periods until it is paid. At a 0% discount rate nothing is discounted, so the present value is simply PMT × n × m.

Example

$1,200 received at the end of every year for 10 years, discounted at 6%:

i ÷ m = 0.06 ÷ 1 = 0.06, and n × m = 10 × 1 = 10 payments
PV = $1,200 × (1 − 1.06⁻¹⁰) ÷ 0.06 = $1,200 × (1 − 0.558395) ÷ 0.06 = $8,832.10
The payments add up to $12,000.00, so the discount is $3,167.90
The first payment is worth $1,200 ÷ 1.06 = $1,132.08 today; the last only $1,200 ÷ 1.06¹⁰ = $670.07
As an annuity due, received at the beginning of each year: $8,832.10 × 1.06 = $9,362.03

How to Use the Annuity Present Value Calculator

"If I'm promised $1,200 at the end of every year for the next 10 years, what is that worth to me today, if I could earn 6% a year on my money elsewhere?" This calculator answers that.

Let's enter the numbers for this example in each box. They are already filled in when the calculator opens, so you can follow along and then change any box to match your own payments.

Payment Amount: Enter 1,200, which is the amount of each payment. If payments are monthly, enter the monthly amount (for example 100, not 1,200). It must be greater than 0.
Payment Interval: Leave it at Annually, which is how often a payment is made. You can also pick Semi-Annually, Quarterly, Monthly or Daily. The discount rate compounds at the same interval.
Payment Timing: Leave it at End (ordinary), which means each payment comes at the end of the year. Pick Beginning (due) if payments come at the start; for this example that gives $9,362.03 instead.
Discount Rate: Enter 6, which is the yearly return in percent you could earn on your money elsewhere. A higher rate makes future payments worth less today. Enter 0 to see the payments without any discount. It must be below 100.
Number of Years: Enter 10, which is how many years the payments last. It must be a whole number from 1 to 100.

Calculate and Reset

Click Calculate to see your results. If a box has a problem, such as a letter in a number box, a message pops up under that box instead. With the default numbers you get:

Your Results: a short summary in words: the payments are worth $8,832.10 today; they add up to $12,000.00, so waiting for them costs $3,167.90, 26.40% of their face value.
Present Value: the headline number, $8,832.10.
Total Payments, Discount, Number of Payments and Value Today vs Face Value: $12,000.00 of payments, a $3,167.90 discount, 10 payments, and the present value as a share of the payments (73.60%).
Chart: one bar for each year's payments. The teal part is what they are worth today and the amber part is the discount; the teal part shrinks the further away the year is, from $1,132.08 in year 1 to $670.07 in year 10.
Yearly Schedule: for each year, the payments, their value today and the discount, with a Total row at the bottom: the values today add up to the present value, $8,832.10. Use Download CSV to open it in a spreadsheet.
Share Results: a link that opens this calculator with your numbers filled in. Copy it, or share it on Facebook or X.

Amounts of $1 million or more are shortened, for example $1.25M. Click Reset to put every box back to its default and show the default results again.

Year	Payments	Value Today	Discount
1	$1,200.00$1,200	$1,132.08$1,132	$67.92$68
2	$1,200.00$1,200	$1,068.00$1,068	$132.00$132
3	$1,200.00$1,200	$1,007.54$1,008	$192.46$192
4	$1,200.00$1,200	$950.51$951	$249.49$249
5	$1,200.00$1,200	$896.71$897	$303.29$303
6	$1,200.00$1,200	$845.95$846	$354.05$354
7	$1,200.00$1,200	$798.07$798	$401.93$402
8	$1,200.00$1,200	$752.89$753	$447.11$447
9	$1,200.00$1,200	$710.28$710	$489.72$490
10	$1,200.00$1,200	$670.07$670	$529.93$530
Total	$12,000.00$12,000	$8,832.10$8,832	$3,167.90$3,168

Annuity Present Value Calculator

Your Results