Annuity due

An annuity due makes each equal periodic payment at the start of a period rather than the end. Its present value equals the ordinary annuity PV multiplied by (1 + r), as every flow is discounted one fewer period.

ByHoang TruongUpdated July 3, 2026

FrameworkTime value of money

See it move

Loading infographic...

An annuity due pays at the start of each period instead of the end, so every cash flow is discounted one fewer period. A five-year ordinary annuity worth €48,000 at 5% becomes an annuity due worth €48,000 × 1.05 = €50,400 — the same payments, just timed one period earlier.

Where it fits

TopicTime Value of MoneyAdvancedSubjectCorporate FinanceAdvanced

The formula

LaTeX

PV = C \times \frac{1-(1+r)^{-n}}{r} \times (1+r)

Variables

$P V$: present value of the annuity-due stream
$C$: equal payment made at the start of each period
$r$: discount rate per period (expressed as a decimal)
$n$: total number of payment periods

Multiply the ordinary annuity PV by (1 + r) to shift each cash flow one period earlier. Lease agreements and insurance premiums commonly follow this pattern.

LaTeX

FV = C \times \frac{(1+r)^n - 1}{r} \times (1+r)

Variables

$F V$: future value of the annuity-due stream at the end of period n
$C$: equal payment made at the start of each period
$r$: interest rate per period (expressed as a decimal)
$n$: total number of payment periods

Because each payment compounds for one extra period compared with an ordinary annuity, the FV is also multiplied by (1 + r).

Check yourself

PracticeCORE

A five-year equipment lease requires payments of €12,000 at the start of each year. The relevant discount rate is 8 per cent. Which expression gives the present value of these payments, and why does it differ from an ordinary annuity?

Select an answer to check your understanding.