Future Value of Annuity Due Formula

What is an annuity due?

An annuity due is a series of equal payments where each payment is made at the beginning of the period instead of the end. That is the only thing that separates it from an ordinary annuity — the amounts and the schedule are otherwise identical.

Payments billed in advance are annuities due in practice: rent, car leases, insurance premiums and many subscriptions all fall due at the start of each period. If you make a savings contribution on the first of the month rather than the last, that stream behaves like an annuity due too. Because the money goes in earlier, it has more time to compound.

The annuity due formula

The future value of an annuity due builds directly on the ordinary annuity formula:

The terms are the same ones used throughout time-value math:

• C — the payment made each period.
• r — the interest rate per period, written as a decimal.
• n — the total number of periods.

The bracket is the ordinary annuity factor; the extra × (1 + r) shifts every payment forward by one period so it earns one more round of interest. As with any compounding calculation, r and n must share a time unit — this site compounds monthly, so r is the annual rate divided by 12 and n is the number of months. For the single-sum growth underneath it all, see the future value formula guide.

Annuity due vs ordinary annuity

The relationship between the two is exact and simple: an annuity due is always worth the ordinary annuity value multiplied by (1 + r).

• Ordinary annuity — each payment lands at the end of the period. This is the default for most loans and investment contributions.
• Annuity due — each payment lands at the beginning, so every payment earns one extra period of interest and the total is higher.

Written side by side, the two are identical except for the final factor:

That last row has a consequence worth stating explicitly: because the whole ordinary value is multiplied by (1 + r), the extra you gain is exactly r × FV_ordinary. In percentage terms the premium for paying early is always the periodic rate — no more, no less — regardless of how many payments there are or how long the schedule runs. The dollar amount grows with the horizon; the percentage does not.

Payment by payment: where the extra comes from

The (1 + r) factor is easier to trust once you have seen it emerge from the individual payments. Take five annual payments of $1,000 at 7 percent — small enough to lay out in full. The only difference between the two columns is how many years each payment has to compound:

Three things fall out of this table. The last ordinary payment earns nothing at all — it arrives at the end of the final period, so it has no time to compound, which is why an ordinary annuity's final payment is worth exactly its face value. Every due column entry is the ordinary entry one row above it, because shifting the schedule forward by one period gives each payment its predecessor's compounding time. And the totals differ by $402.55, which is precisely 7 percent of $5,750.74.

Both formulas reproduce these totals exactly: $1,000 × [(1.07⁵ − 1) ÷ 0.07] = $5,750.74, and multiplying by 1.07 gives $6,153.29. Summing the payments individually and applying the closed formula are the same calculation, which is the whole reason the formula exists.

Worked example: $500 a month

Here is $500 a month at 7 percent, compounded monthly, shown both ways. The “extra” column is what the beginning-of-period timing adds versus an ordinary annuity.

In every case the paid-in amount is identical — $60,000, $120,000 and $180,000 respectively. The annuity due ends higher purely because each payment compounds for one more month.

Why the premium is bigger with annual payments

The $1,519 the monthly example gains over 20 years is real but modest — about half a percent. That is not because the horizon is short. It is because the periodic rate is small: a monthly rate of 7% ÷ 12 is 0.583 percent, so the timing premium is 0.583 percent. Keep the annual outlay at $6,000 and the annual return at 7 percent, and simply change how often the money goes in:

All three rows pay in the same $120,000 over the same 20 years. The timing premium ranges from $1,519 to $17,218 — more than eleven times larger — entirely because the period is longer. Paying a year early is worth a year of interest; paying a month early is worth a month of interest.

There is a second effect in the table that is easy to miss. Read down the ordinary column and more frequent payments win: $260,463 monthly against $245,973 annually, because monthly money starts compounding sooner on average. Read down the due column and the ranking reverses, with annual slightly ahead at $263,191. An annuity due paid annually puts the entire $6,000 to work on day one of each year, which beats spreading it out. So “pay more often” and “pay at the start” are two separate levers, and the second one is worth more when the periods are long.

Calculating it without the algebra

You rarely need to apply the formula by hand. Match the situation to the right tool:

• Level payments, either timing — the future value of annuity calculator handles both ordinary and annuity due with a toggle.
• In a spreadsheet — Excel and Google Sheets express the timing as the final type argument of FV: =FV(0.07/12,240,-500,0,1) returns $261,983 for the annuity due, against $260,463 with the default 0. The Excel guide covers the rest of the arguments.
• Payments that grow each year — the growing annuity calculator steps the payment up over time.

Each applies the same math shown here, so the figures will line up with the formula.

Assumptions

• Constant payment and rate. The formula assumes every payment is equal and the rate holds steady for the whole term.
• Matched periods. r and n share a time unit — monthly rate with months here, since this site compounds monthly.
• Payments at the start of the period. That beginning-of-period timing is exactly what the × (1 + r) factor accounts for.
• Nominal figures. Results are before inflation and tax, both of which reduce real growth.

How these figures were checked

This page makes no claims that require an outside source — every number is arithmetic, so it can be verified rather than cited:

• Both routes agree. The five-payment table was computed by growing each payment individually, C × (1 + r)periods, and summing; the closed formula was computed separately. They match to the cent, which is the test that the (1 + r) factor is doing what it claims.
• Rate conventions. Monthly figures use r = 0.07 ÷ 12 with n in months; quarterly use 0.07 ÷ 4 with n in quarters; annual use 0.07 with n in years. Rates are nominal annual rates, not effective ones.
• Precision. Everything is carried at full precision and rounded only for display, so the timing premiums are differences of exact values rather than differences of rounded ones.
• Identity check. Each timing premium was confirmed to equal the periodic rate times the ordinary value — the algebraic prediction — rather than being computed independently and assumed to agree.

The 7 percent rate is an illustrative assumption, not a forecast. Last verified 8 September 2026.

Frequently asked questions

The bottom line

The future value of an annuity due formula is just the ordinary annuity formula with one extra step: multiply by (1 + r) to account for payments arriving at the start of each period. That single factor is why paying in advance always ends ahead — every payment compounds one period longer.

When you would rather not run the algebra, the future value of annuity calculator switches between ordinary and annuity-due timing for you, and the future value formula guide covers the single-sum growth underneath it.