Future Value Of Annuity Due Calculator

What this calculator does

This calculator works out what a stream of equal payments grows into, where each payment is made at the beginning of its period rather than the end. That arrangement has a name, an annuity due, and this tool is built specifically for it.

Everything here turns on timing. The amounts are the same, the rate is the same, the number of payments is the same. The only thing that changes is that the money arrives early, at the top of each period instead of the bottom. It sounds like a technicality. It is worth real money, and the amount it is worth turns out to be beautifully precise.

What "due" means: paying at the start, not the end

Annuities come in two timings, and the whole vocabulary rests on this one distinction. In an ordinary annuity, the payment lands at the end of each period, so there is a gap between the clock starting and the first payment arriving. In an annuity due, the payment lands at the beginning, so the first one is handed over immediately, before any time has passed at all.

That head start applies to every payment in the series, not just the first. Each one arrives a full period earlier than its ordinary-annuity counterpart, which means each one gets a full extra period to sit and earn. Since the money is going in sooner and coming out never, the total at the end has to be larger. The question is by exactly how much, and the answer is unusually clean.

How to use it

1. Amount of equal payments. The amount paid in at the start of each period.
2. Interest rate per period. The rate earned in one period, matched to whatever your period is.
3. Number of periods. How many payments will be made.

Press Calculate for the future value, or Reset to clear the fields. Before you do, make sure the beginning-of-period assumption actually matches your arrangement, because if your payments land at the end of each period, the ordinary annuity calculator is the right tool and this one will overstate your total.

A worked example you can check

Take 1,000 paid in at the start of every period, earning 6 percent a period, for 10 periods. To make the timing effect visible, here it is alongside the same payments made at the end of each period instead.

• Paid at the end of each period, an ordinary annuity: 13,180.79
• Paid at the beginning of each period, an annuity due: 13,971.64
• What the earlier timing was worth: 790.85

Same 10,000 of your own money in both cases, same rate, same number of payments. Simply handing the money over at the start of each period rather than the end produced an extra 790.85. That figure is not a rounding artefact or a rule of thumb. It is exactly one thing, as the next section shows.

The whole difference is one extra period of interest

The relationship between the two timings is exact, and once you see it you will never need to look it up again. The future value of an annuity due is simply the ordinary annuity total multiplied by one plus the rate:

Future value of annuity due = Future value of ordinary annuity × (1 + rate)

Check it on the example: 13,180.79 × 1.06 = 13,971.64. It lands precisely. And that means the extra 790.85 is nothing more mysterious than 6 percent of 13,180.79, which is to say a single period's interest on the entire ordinary-annuity total. Every payment moved one period earlier, so the whole pile effectively earns one extra period of interest, and multiplying by (1 + rate) is exactly what applying one more period of interest looks like.

This gives you a rule you can carry anywhere. The reward for paying at the start rather than the end is one period's interest on the total, no more and no less. At low rates that is a modest bonus. At higher rates, or on a large accumulated pot, it becomes a serious sum for doing nothing but moving the date. It also tells you which direction the error goes if you pick the wrong tool: using the ordinary annuity when your payments are actually made at the start understates your result by that same one period of interest.

Which kind is your arrangement?

Since the timing is the whole game, it is worth being able to spot which one you are dealing with. The rough test is whether you pay for the period before you use it or after.

Things typically paid at the beginning, and so annuities due: rent, which is paid at the start of the month you are about to live in; insurance premiums, paid before the cover applies; lease payments; and subscriptions. Saving works this way too whenever you move money at the start of the month, on payday, rather than at the end. Things typically paid at the end, and so ordinary annuities: most loan and mortgage instalments, salaries paid for a month already worked, and bond coupons paid after the interest has been earned.

There is a small piece of practical wisdom hiding in that list. If you save at the start of each month instead of whatever is left at the end, you are running an annuity due rather than an ordinary annuity, and this calculator, not the other one, is the one that describes your money. The extra you collect for the habit is precisely one period's interest on the whole balance, every single period.

Questions people ask

What is the difference between an annuity due and an ordinary annuity?

Only the timing of the payments. An annuity due pays at the beginning of each period, an ordinary annuity at the end. That single period of difference is the entire distinction.

How much more is an annuity due worth?

Exactly one plus the rate, times the ordinary annuity total. The extra amount equals one period's interest on that total, so a 6 percent rate makes an annuity due 6 percent larger.

What are real examples of an annuity due?

Rent, insurance premiums, leases, and subscriptions are usually paid at the start of the period. Saving on payday rather than at month end is also an annuity due.

What happens if I use the wrong calculator?

You will be out by exactly one period of interest. Using the ordinary annuity for beginning-of-period payments understates the total, and using this one for end-of-period payments overstates it.

References

The distinction between an ordinary annuity, whose first cash flow occurs at the end of the first period, and an annuity due, whose payments begin immediately, follows OpenStax's finance text, which describes the gap between the two as one period, that is, a single additional period of interest. The multiplication of the ordinary annuity result by one plus the periodic rate is the standard adjustment for that shift.

1. OpenStax, Principles of Finance, 8.2 Annuities. https://openstax.org/books/principles-finance/pages/8-2-annuities
2. OpenStax, Principles of Finance, 8.5 Equal Payments with a Financial Calculator and Excel. https://openstax.org/books/principles-finance/pages/8-5-equal-payments-with-a-financial-calculator-and-excel