Present Value of Annuity Due Calculator
Find the present value of an annuity due — equal payments made at the start of each period, like rent or lease payments paid in advance.
How it works
PV(due) = PMT · [1 − (1 + i)^−n] / i · (1 + i)
An annuity due pays at the beginning of each period rather than the end, which is how rent, leases and many insurance premiums actually work. Because every payment arrives one period sooner than in an ordinary annuity, each is discounted less, so the present value is exactly (1 + i) times the ordinary-annuity value. That single (1 + i) factor is the whole difference between the two annuity types.
Worked example
Ten yearly payments of $1,000 at the start of each year, discounted at 5%, first give the ordinary PV = 1,000 · [1 − 1.05^−10] / 0.05 = $7,721.73. Multiplying by 1.05 gives the annuity-due PV = $8,107.82.
Sources: Annuity (finance theory) — Wikipedia
Frequently asked questions
What makes an annuity “due” rather than “ordinary”?
An annuity due pays at the start of each period; an ordinary annuity pays at the end. Rent and leases are usually annuities due because you pay for the coming period in advance.
Why is an annuity due worth more?
Every payment happens one period earlier, so it is discounted by one fewer period. Money received sooner is worth more, and the effect is captured exactly by multiplying the ordinary present value by (1 + i).
What if the interest rate is zero?
With a 0% rate there is no discounting, so the present value is simply the payment times the number of payments, and the ordinary and due values are identical. This calculator handles that case without dividing by zero.
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Educational financial-math tool, not investment or financial advice.