Future Value of Annuity Due Formula
The future value of an annuity due formula is FV = C × [((1 + r)n − 1) / r] × (1 + r). It gives what a series of equal payments grows to when each payment is made at the beginning of every period rather than the end. That extra (1 + r) is the whole difference from an ordinary annuity: because every payment arrives a period earlier, each one earns one more period of interest. At 7 percent compounded monthly, $500 a month for 20 years grows to about $261,983 as an annuity due — roughly $1,519 more than the same payments made at the end of each month.
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.
The gap looks small on any single payment but compounds across the whole schedule. Over long horizons and larger payments it becomes a meaningful difference, as the worked example below shows.
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.
| Horizon | Ordinary annuity | Annuity due | Extra from due |
|---|---|---|---|
| 10 years | $86,542 | $87,047 | $505 |
| 20 years | $260,463 | $261,983 | $1,519 |
| 30 years | $609,985 | $613,544 | $3,558 |
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.
Switch timings instantly: the future value of annuity calculator has an ordinary / annuity-due toggle, so you can compare both without touching the formula.
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.
- End-of-period payments only — the future value of ordinary annuity calculator focuses on the ordinary case.
- 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.
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 of money formula guide covers the single-sum growth underneath it.
Disclaimer: This guide is for general educational purposes only and is not financial advice. The examples use assumed rates of return to illustrate the formula; they are projections, not guarantees, and actual results vary with markets, inflation, taxes and fees. Consider speaking with a qualified financial professional before making decisions about your own money.