Annuity due vs ordinary annuity: what the timing difference actually costs

An ordinary annuity pays at the end of each period. An annuity due pays at the beginning. That is the whole difference, and everything else follows from it: because each payment in an annuity due arrives one period earlier, both its present value and its future value are exactly the ordinary annuity's value multiplied by (1 + r), where r is the interest rate for one period.

The distinction sounds academic until you notice which real contracts fall into which category. Rent, insurance premiums and lease payments are annuities due — you pay before you occupy the flat or hold the cover. Loan repayments, bond coupons and most retirement income streams are ordinary annuities — the payment comes after the period it relates to. Getting the timing wrong in a valuation does not produce a wildly wrong answer, but it produces a consistently wrong one, always in the same direction.

This article works through the mechanics, the formulas, a worked comparison, and the places the distinction genuinely matters in annuity and settlement contracts.

The timing difference, drawn out

Take five annual payments of $1,000 and imagine a timeline running from today (time 0) to the end of year 5.

An ordinary annuity places payments at the end of years 1, 2, 3, 4 and 5. Nothing happens today. The last payment lands exactly five years from now.

An annuity due places payments at the beginning of years 1 through 5 — which is time 0, 1, 2, 3 and 4. The first payment is in your hand immediately. The last one arrives four years from now, not five.

Same number of payments, same amount each, one period of difference on every single one. In an annuity due you hold the money longer, so if you are receiving, an annuity due is worth more. If you are paying, it costs you more.

Two terms you will see used interchangeably with these:

Ordinary annuity	Annuity due
Annuity in arrears	Annuity in advance
Payment at period end	Payment at period start
Loans, bonds, most pensions	Rent, leases, premiums, immediate annuity income

The formulas and why (1 + r) is the only change

The present value of an ordinary annuity is the standard textbook expression:

PV (ordinary) = PMT × [1 − (1 + r)⁻ⁿ] ÷ r

where PMT is the payment per period, r is the periodic interest rate (annual rate divided by the number of periods per year) and n is the total number of payments.

For an annuity due, you do not need a separate formula. Every cash flow is discounted for one period less, so you compound the whole result forward by one period:

PV (due) = PV (ordinary) × (1 + r)

The same relationship holds for future value:

FV (ordinary) = PMT × [(1 + r)ⁿ − 1] ÷ r

FV (due) = FV (ordinary) × (1 + r)

This is why financial calculators have a BGN/END toggle rather than two sets of keys, and why spreadsheet functions such as PV, FV and PMT take a final "type" argument: 0 for end-of-period, 1 for beginning-of-period. Setting that argument is the entire adjustment. If you are running the numbers yourself, the present value of annuity calculator and future value of annuity calculator handle both conventions.

A worked comparison (illustrative figures only)

Assume $1,000 a year for 10 years at a 5% annual interest rate. These are worked examples with stated assumptions, not quotes for any product.

Present value

• Ordinary annuity factor: [1 − 1.05⁻¹⁰] ÷ 0.05 = 7.7217
• PV = $1,000 × 7.7217 = $7,721.73
• Annuity due: $7,721.73 × 1.05 = $8,107.82
• Difference: $386.09, about 5% — which is exactly the interest rate, as the formula promises.

Future value at the end of year 10

• Ordinary annuity factor: [1.05¹⁰ − 1] ÷ 0.05 = 12.5779
• FV = $1,000 × 12.5779 = $12,577.89
• Annuity due: $12,577.89 × 1.05 = $13,206.79
• Difference: $628.89

Now something closer to a real income stream. Assume $2,000 a month for 20 years (240 payments) discounted at 4% a year, so r = 0.04 ÷ 12 = 0.003333 per month:

• Ordinary annuity: PV ≈ $330,040
• Annuity due: PV ≈ $331,140
• Difference: about $1,100

Notice how the gap shrank in percentage terms. With monthly payments, one period is one month, so the adjustment is one month's interest rather than a full year's. The shorter the period, the smaller the practical impact of getting the convention wrong — which is precisely why the error so often goes unnoticed in monthly contracts and shows up glaringly in annual ones.

Rates, discount rates and product terms change constantly. Treat every figure above as arithmetic illustrating a method, and verify any real valuation against actual contract terms before acting on it.

Which convention real annuity contracts use

Insurance contracts are not consistent, and the paperwork does not always say plainly which one applies. A few reliable patterns:

Immediate annuity income is usually an annuity due. When you hand an insurer a premium for a single premium immediate annuity, income typically starts one payment interval later, but many contracts are written so the payment falls due at the start of each period. Because this works in the buyer's favour, the same premium buys a slightly smaller payment than an end-of-period design would.

Working the last example backwards makes the point. A $100,000 premium spread over 240 monthly payments at 4% would support roughly $606 a month paid at each month's end, or about $604 a month paid at each month's start. The insurer is not being generous or stingy — it is the same $100,000, priced for the timing.

Loan amortisation is an ordinary annuity. Interest accrues over the month, then you pay. This is why a mortgage schedule always shows the first payment one full month after drawdown.

Deferred annuity accumulation depends on when you fund it. If you pay premiums at the start of each year during the deferral phase, you are building up an annuity due; at the end, an ordinary annuity. Over a 20- or 30-year accumulation period, one extra year of compounding on every contribution is not trivial.

Structured settlement payment schedules vary by design. Some start immediately on court approval, some after a deferral. Whichever it is, the discounting convention has to match, or the valuation drifts.

If you are comparing contracts, the practical move is to read the payment-commencement language rather than assuming. Two quotes that look different may simply be quoting different conventions. Our guide to annuity payout options covers the other structural choices that move a quoted payment, and immediate vs deferred annuities explains how the deferral period itself changes the arithmetic.

Where the distinction matters most

Three situations where the (1 + r) factor stops being a rounding detail:

Long horizons with annual periods. A 30-year stream valued annually carries the full annual rate as the adjustment. At a 6% discount rate, that is a 6% valuation difference — more than most people's margin for error when comparing offers.

High discount rates. The adjustment scales directly with r. In secondary-market settlement transfers, where discount rates run far above prevailing savings rates, the timing convention shifts the number materially. If you are valuing a payment stream, see how the structured settlement discount rate drives the result before worrying about anything else.

Lease-versus-buy and pension lump-sum decisions. Leases are almost always annuities due; the loan alternative is an ordinary annuity. Comparing them without adjusting compares two different things.

Conversely, the distinction matters least for monthly streams at modest rates over short periods — the case most household budgeting falls into.

How to avoid getting it wrong

A short checklist:

1. Ask when the first payment lands. Today or at period end? That single answer settles the convention.
2. Match the rate to the period. Monthly payments need a monthly rate and a monthly count. Mixing an annual rate with monthly payments is a much larger error than the due-versus-ordinary question.
3. Set the type argument. In a spreadsheet, the final argument of PV, FV, PMT, RATE and NPER is 0 for ordinary and 1 for due. Leaving it blank defaults to ordinary.
4. Sanity-check the direction. As a receiver, the annuity due figure must be the larger one. If your annuity due value comes out below the ordinary value, you have applied the factor the wrong way.
5. Keep the assumptions written down. Rate, period count, convention and start date. A valuation without its assumptions is not a valuation.

Frequently asked questions

Is an annuity due always worth more than an ordinary annuity?

To the person receiving the payments, yes — as long as the interest rate is positive. Each payment arrives one period sooner, so it is discounted one period less. The value is higher by exactly the factor (1 + r). To the person making the payments, the annuity due is correspondingly more expensive, for the same reason.

Which type is a retirement annuity?

It depends on the contract, and you have to read it. Income from an immediate annuity is often structured as an annuity due, with the payment falling at the start of each period. Payments from a pension or a deferred contract are more commonly in arrears. The contract's payment-commencement clause tells you; the marketing brochure usually does not.

How do I switch between the two in a spreadsheet?

Use the "type" argument. =PV(rate, nper, -pmt, 0, 0) gives the ordinary annuity value and =PV(rate, nper, -pmt, 0, 1) gives the annuity due value. The same applies to FV and PMT. On a financial calculator, it is the BGN/END mode toggle — and it is worth checking which mode the calculator is in before you start, because it persists between calculations.

Does the difference matter for monthly payments?

Less than for annual ones. The adjustment is one period's interest, so a monthly stream at 4% a year carries roughly a 0.33% adjustment rather than 4%. It is still worth getting right in a formal valuation, but it will rarely change a decision on its own. Over a long accumulation period with annual contributions, it can.

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This article explains the mechanics of annuity timing conventions for educational purposes. It is not personal financial, tax or investment advice, and the figures used are worked examples based on the stated assumptions rather than quotes for any product. Actual rates, payment schedules and contract terms vary and change over time — check the contract and speak to a qualified adviser before relying on any valuation.