What is the formula for the present value of an annuity due?

PVdue = P × [1 − (1 + r)−n] ÷ r × (1 + r). It is the ordinary annuity value multiplied by (1 + r).

Why is an annuity due worth more?

Each payment arrives one period sooner, so it is discounted for one period less and is worth more today.

What are examples of annuities due?

Rent paid at the start of the month, lease payments, insurance premiums and payouts that begin immediately.

How do I calculate it in Excel?

Use =PV(rate, nper, pmt, 0, 1). The type argument 1 tells Excel the payments are at the beginning of each period.

Present Value of Annuity Due Formula

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Present Value of an Annuity Due Calculator

An annuity due is a stream of equal payments made at the beginning of each period rather than the end. Rent, lease payments, insurance premiums and many lottery or pension payouts work this way. Because each payment arrives one period earlier than in an ordinary annuity, it is discounted one period less, so its present value is higher by exactly a factor of (1 + r).

Formula

PV_due = P × 1 − (1 + r)⁻ⁿr × (1 + r)

Where

PV: present value of the payment stream (payments at the start of each period)
P: payment per period
r: interest rate per period, as a decimal
n: number of payments

Calculator

Payment per period (P)

Rate per period (r) (%)

Annual rate ÷ payments per year.

Number of payments (n)

Result and step-by-step solution

Present value of the annuity due

8,107.82

10 payments of 1,000.00 (total paid in 10,000.00).

Convert the rate to a decimal
r = 5% = 0.05
Discount term
(1 + r)⁻ⁿ = (1 + 0.05)⁻¹⁰ = 0.613913
Annuity factor
1 − 0.6139130.05 = 7.721735
Multiply by the payment
1,000.00 × 7.721735 = 7,721.73 (ordinary annuity)
Shift payments to the start of each period
7,721.73 × (1 + 0.05) = 8,107.82

How to use the formula

The calculator first works out the ordinary annuity value, P × [1 − (1 + r)⁻ⁿ] ÷ r, and then multiplies by (1 + r). An equivalent way to see it: the first payment is received today at full value, and the remaining n − 1 payments form an ordinary annuity.

With 10 payments of 1,000 at 5%, the annuity due is worth 8,107.82 compared with 7,721.73 for the ordinary annuity. That gap matters when you value a lease or compare a lump-sum buyout with payments that start immediately. Spreadsheet users get the same answer from PV(rate, nper, pmt, 0, 1), where the final 1 means payments at the beginning. For the savings side, see the future value of an annuity due.

Frequently asked questions

What is the formula for the present value of an annuity due?: PV_due = P × [1 − (1 + r)⁻ⁿ] ÷ r × (1 + r). It is the ordinary annuity value multiplied by (1 + r).
Why is an annuity due worth more?: Each payment arrives one period sooner, so it is discounted for one period less and is worth more today.
What are examples of annuities due?: Rent paid at the start of the month, lease payments, insurance premiums and payouts that begin immediately.
How do I calculate it in Excel?: Use =PV(rate, nper, pmt, 0, 1). The type argument 1 tells Excel the payments are at the beginning of each period.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.