Present Value of Annuity Calculator
Calculate the present value of an ordinary annuity, annuity due, growing annuity or perpetuity based on payment amount, rate and timing.
Calculate Present Value of Annuity
Time period
Interest
Cash flow (annuity payments)
| Result | Value |
|---|
For a perpetuity, enter “p” or “perpetuity” in the number of periods field.
How the present value of annuity calculator works
The present value of annuity calculator works by discounting a series of equal or growing payments back to today using a chosen interest rate and compounding frequency. You enter the payment amount, interest rate, number of periods, compounding, and whether payments occur at the start or end of each period, and the calculator returns the equivalent lump sum value today.
Ordinary annuity versus annuity due
Ordinary annuity versus annuity due is determined by the payment timing setting. An ordinary annuity pays at the end of each period, while an annuity due pays at the beginning. Because annuity due payments arrive sooner, they are worth more today, so the present value is multiplied by an extra factor of 1 plus i.
Present value of annuity formula explained
The present value of annuity formula for level payments is PV equals PMT divided by i, times the quantity 1 minus 1 divided by the quantity 1 plus i raised to n. Here PMT is the payment per period, i is the rate per compounding period, and n is the total number of payments. For an annuity due, this result is multiplied by 1 plus i.
Worked example for an ordinary annuity
Worked examples make the formula concrete. For a payment of $1,000 per year at 8 percent annual interest for 10 years, i equals 0.08 and n equals 10. The present value works out to approximately $6,710.08 for an ordinary annuity received at the end of each year.
Growing annuities and perpetuities
Growing annuities and perpetuities extend the basic formula. A growing annuity increases each payment by a fixed growth rate g, and its present value uses a modified formula that subtracts g from i in the denominator. A perpetuity removes the time limit entirely, so as the number of periods approaches infinity, the present value simplifies to PMT divided by i.
When to use a perpetuity calculation
When to use a perpetuity calculation depends on whether payments are expected to continue indefinitely, such as certain preferred stock dividends or endowment distributions. Entering “p” for the number of periods switches the calculator to the perpetuity formula automatically.
Reference table of annuity variables
| Variable | Meaning |
|---|---|
| PMT | Payment amount per period |
| G, g | Growth rate of payments, g = G / 100 |
| R, r | Annual nominal interest rate, r = R / 100 |
| m | Compounding frequency per period |
| q | Number of payments per period |
| i | Rate per payment interval |
| n | Total number of payments |
| T | 0 for ordinary annuity, 1 for annuity due |
| PV | Present value of the annuity |
Frequently asked questions
The present value of an annuity is the current worth of a series of equal future payments, discounted at a given interest rate. It tells you how much a stream of regular payments is worth today instead of receiving each payment individually over time.
An ordinary annuity makes payments at the end of each period, while an annuity due makes payments at the beginning of each period. Because annuity due payments are received earlier, the present value of an annuity due is always higher than an otherwise identical ordinary annuity.
The formula for present value of an ordinary annuity is PV equals PMT divided by i, multiplied by the quantity 1 minus 1 divided by the quantity 1 plus i raised to n, where PMT is the payment amount, i is the rate per period, and n is the total number of payments.
A growing annuity is a series of payments that increase by a fixed percentage each period rather than staying constant. The present value of a growing annuity uses a modified formula that accounts for both the discount rate and the growth rate of the payments.
A perpetuity is an annuity that continues forever with no end date. The present value of a perpetuity simplifies to the payment amount divided by the interest rate per period, since the number of periods approaches infinity and the discount factor approaches zero.
Payment frequency affects present value because more frequent payments, such as monthly instead of annually, change both the rate per payment period and the total number of payments used in the calculation. Generally, more frequent compounding combined with more frequent payments produces a different present value than annual payments at the same nominal rate.