Ordinary Annuity

Ordinary Annuity — Definition and Key Points

An ordinary annuity is a series of equal payments made at the end of each period for a fixed number of periods. Periods can be monthly, quarterly, semiannually, or annually. Common examples include bond coupon payments, many dividend schedules, and loan or mortgage payments when they are due at period end.

Key points:
* Payments occur at the end of each period.
* Present value depends on the discount (interest) rate: higher rates lower present value; lower rates raise it.
* An annuity due is similar but pays at the beginning of each period and therefore has a higher present value (all else equal).
* The term “annuity” can also refer to insurance products, but “ordinary annuity” here describes timing of periodic cash flows, not the insurance contract.

How It Works

The value of an ordinary annuity is determined by the size of the periodic payment, the number of periods, and the interest (discount) rate. Because of the time value of money, cash received later is worth less than the same cash received sooner. The present value (PV) of an ordinary annuity is the amount you would need today to replicate those future payments, given a specific interest rate.

Present Value Formula

Let:
* PMT = periodic payment
* r = interest rate per period (decimal)
* n = total number of periods

Present value of an ordinary annuity:
PV = PMT × [1 − (1 + r)^−n] / r

Example:
A plan pays $50,000 at the end of each year for 5 years. If the discount rate is 7%:
1. Compute the annuity factor: [1 − (1 + 0.07)^−5] / 0.07 ≈ 4.1002
2. PV = $50,000 × 4.1002 ≈ $205,010

Annuity Due vs. Ordinary Annuity

An annuity due makes payments at the beginning of each period. Because payments arrive earlier, an annuity due is worth more than an ordinary annuity (for the same PMT, r, and n).

You can convert PV of an ordinary annuity to the PV of an annuity due by multiplying by (1 + r):
PV_due = PV_ord × (1 + r)
Using the example above:
* PV_ord ≈ $205,010
* PV_due ≈ $205,010 × 1.07 ≈ $219,360

Practical implication: recipients prefer annuity-due timing (get paid sooner); payers prefer ordinary annuity timing (pay later).

Practical Uses and Examples

Common ordinary annuity examples:
* Bond coupon payments (often semiannual)
* Dividends paid at period end
* Loan or mortgage payments scheduled at the end of each month

When evaluating offers or contracts with periodic payments, check whether payments occur at period-start (annuity due) or period-end (ordinary annuity) — the timing changes valuation and effective yield.

Takeaways

• An ordinary annuity = equal payments at the end of each period.
• Present value is calculated with PV = PMT × [1 − (1 + r)^−n] / r.
• Rising interest rates reduce the present value of future annuity payments.
• An annuity due (payments at period start) has a higher PV than an ordinary annuity because funds are received sooner.