In finance, an annuity is any series of equal payments made at regular intervals. Whether those payments arrive at the beginning or end of each period determines whether it is an ordinary annuity or an annuity due — a distinction that affects the present and future value of the payment stream.
The Core Difference
| Ordinary annuity | Annuity due | |
|---|---|---|
| Payment timing | End of each period | Beginning of each period |
| Also called | Annuity in arrears | Annuity in advance |
| Common examples | Mortgage, bond coupons, most retail annuity income | Rent, lease, insurance premiums |
| Present value | Lower (each payment discounted one more period) | Higher (each payment discounted one fewer period) |
| Future value | Lower | Higher |
Timeline Illustration
For a 3-period annuity with payments of $1,000 and a 5% annual rate:
Ordinary annuity (payments at period END):
- Period 0 | Period 1 ($1,000) | Period 2 ($1,000) | Period 3 ($1,000)
Annuity due (payments at period START):
- Period 0 ($1,000) | Period 1 ($1,000) | Period 2 ($1,000) | Period 3
The annuity due gets the first payment immediately. Each payment arrives one period earlier than in the ordinary annuity.
Present Value Formulas
Ordinary annuity present value: PV = PMT x [1 - (1 + r)^(-n)] / r
Annuity due present value: PV = PMT x [1 - (1 + r)^(-n)] / r x (1 + r)
The annuity due formula is simply the ordinary annuity formula multiplied by (1 + r) — reflecting the one extra period each payment earns before being received.
Example — Present value of $1,000/year for 5 years at 5%:
- Ordinary annuity PV = $1,000 x [(1 - 1.05^-5) / 0.05] = $1,000 x 4.3295 = $4,329.48
- Annuity due PV = $4,329.48 x 1.05 = $4,545.95
The annuity due is worth $216.47 more in present value terms.
Future Value Formulas
Ordinary annuity future value: FV = PMT x [(1 + r)^n - 1] / r
Annuity due future value: FV = PMT x [(1 + r)^n - 1] / r x (1 + r)
Example — Future value of $1,000/year for 5 years at 5%:
- Ordinary annuity FV = $1,000 x [(1.05^5 - 1) / 0.05] = $1,000 x 5.5256 = $5,525.63
- Annuity due FV = $5,525.63 x 1.05 = $5,801.91
Which Type Are Real-World Annuities?
Mortgage payments — Ordinary annuity (payment due at end of each month after one full month of interest accrual)
Bond coupons — Ordinary annuity (interest accrues first; coupon paid at period end)
Retail retirement annuities (SPIA, fixed, variable) — Typically ordinary annuities; most contracts pay at the end of the payment period. Some contracts offer a choice.
Rent/lease — Annuity due (payment due at the start of the rental period)
Insurance premiums — Annuity due (premium paid in advance for the upcoming coverage period)
Practical Importance for Retirement Planning
For most retail annuity buyers, whether your SPIA pays at the start or end of the month has a small real-world impact (one month’s timing on a payment stream that may last 20+ years). The distinction matters much more for:
- Financial calculations in time-value-of-money problems (finance courses, actuarial math)
- Mortgage vs lease comparison (choosing when payments hit)
- Annuity contract review — understanding whether your contract defaults to payment at month start or month end, and whether it affects your income plan
Understanding payment timing structures is part of the annuities hub. See how accumulation periods work in what is an annuity accumulation period, and learn the broader terminology in common annuity terms.
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