Annuity

An annuity is a series of equal cash flows paid or received at regular intervals for a fixed number of periods, such as loan repayments. Its present value uses an annuity factor rather than discounting each flow separately.

ByHoang TruongUpdated June 30, 2026

FrameworkTime value of money

See it move

Loading infographic...

An annuity is a stream of equal payments — say €2,000 a year for four years at 5%. Instead of discounting each payment separately, an annuity factor of 3.546 collapses all four calculations into one multiplier: €2,000 × 3.546 ≈ €7,092 present value.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

The formula

LaTeX

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

Variables

$P V$: Present value of the annuity (€)
$P M T$: Equal payment per period (€)
$r$: Discount rate per period (decimal)
$n$: Number of periods (periods)

Values a stream of equal periodic payments as a single present-day sum (ordinary annuity, payments at end of period).

Check yourself

PracticeCORE

An ordinary annuity pays €1,500 at the end of each year for four years. The discount rate is 6% per annum. The four-year annuity factor at 6% is 3.465. What is the present value of this annuity?

Select an answer to check your understanding.