Present Value of Annuity Calculator

Q: What is the present value of annuity formula?

For an ordinary annuity, the formula is PV = PMT × [1 - (1 + i)^-n] / i. For an annuity due, multiply that result by (1 + i) because the payments happen at the beginning of each period.

Calculate the present value of a series of future payments using a discount rate, payment frequency, and annuity type.

Use this present value of annuity calculator to find what a series of future payments is worth today. Enter the payment amount, discount rate, number of years, payment frequency, and choose whether payments occur at the beginning or end of each period.

What is the Present Value of an Annuity?

Present value of an annuity is the value today of a stream of equal payments received or paid over time. Instead of valuing one future lump sum, it discounts many scheduled payments back to the present and combines them into one current value.

Present Value of Annuity Formula

For an ordinary annuity, the standard formula is PV = PMT × [1 - (1 + i)^-n] / i. For an annuity due, the result is multiplied by (1 + i) because each payment happens one period earlier.

Ordinary Annuity vs Annuity Due

An ordinary annuity assumes payments happen at the end of each period. An annuity due assumes payments happen at the beginning of each period, so each payment is discounted for one less period and the present value is higher.

Example Calculation

Suppose the periodic payment is 1,000, the annual discount rate is 5%, the term is 10 years, the payment frequency is annually, and the annuity type is ordinary annuity.

PV = 1,000 × [1 - (1 + 0.05)^-10] / 0.05
PV ≈ 7,721.73

This means that receiving 1,000 per year for 10 years is worth about 7,721.73 today if the discount rate is 5%.

If payments are made at the beginning of each period, the annuity due value is higher because each payment is discounted for one less period.

When to Use Present Value of Annuity

Use present value of annuity when you want to evaluate a pension stream, rental payments, lease cash flows, settlement installments, or any equal payment series in today’s money. It is useful whenever timing matters and you want to compare recurring payments with a single amount today.

If you need a broader tool with more time-value options, use the advanced present and future value calculator.

Present value of annuity formula

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

$$PV_{due} = PMT \times \frac{1-(1+i)^{-n}}{i}\times(1+i)$$

Initial Data

Periodic payment

Annual discount rate

Number of years

Payment frequency

Annually Semi-annually Quarterly Monthly

Payment timing

end of period (ordinary annuity) start of period (annuity due)

Result

Present value of annuity:

Total payments:

Periodic payment
Annual discount rate
Number of years
Payment frequency
Payment timing
Total discount
Number of payments
Effective periodic discount rate

FAQ

What is the present value of an annuity?
It is the value today of a series of equal future payments. The calculation discounts each payment back to the present and adds them together into one current amount.

How do you calculate the present value of an annuity?
You use the periodic payment, discount rate, number of payments, and payment timing. This calculator first converts the annual rate into a periodic rate, then applies the ordinary annuity or annuity due formula.

What is the present value of annuity formula?
For an ordinary annuity, the formula is PV = PMT × [1 - (1 + i)^-n] / i. For an annuity due, multiply that result by (1 + i) because the payments happen at the beginning of each period.

What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity assumes payments happen at the end of each period. An annuity due assumes payments happen at the beginning, which makes each payment more valuable in present-value terms.

Why is an annuity due worth more than an ordinary annuity?
Each annuity-due payment arrives one period earlier, so it is discounted less. Because all payments are shifted earlier, the total present value is higher than for an otherwise identical ordinary annuity.

What discount rate should I use?
Use a rate that reflects your required return, opportunity cost, or the rate appropriate for the cash flows you are valuing. The right choice depends on the purpose, but the calculator works the same way once you set the rate.

What is the difference between present value and present value of annuity?
Present value usually refers to one future amount discounted back to today. Present value of annuity applies the same discounting idea to a whole series of equal payments instead of one lump sum.

When should I use a present value of annuity calculator?
Use it when you want to value pensions, leases, installments, rental agreements, or any equal recurring payment stream. It is especially useful when comparing a stream of payments with a one-time amount today.