What is the future value of an annuity?

The accumulated value at a future date of a stream of equal periodic payments compounded at a stated interest rate. It's the math that underlies 401(k) projections, savings goals, and education-funding planning. Formula: FV = PMT × [(1+r)^n − 1] / r, where r is rate per period and n is total periods.

What's the difference between ordinary annuity and annuity due?

Ordinary annuity: payments made at the END of each period (typical for mortgages, bonds, and most savings programs). Annuity due: payments at the BEGINNING (typical for rent, insurance premiums, leases). Annuity due has slightly higher FV because each payment compounds for one extra period. Multiply the ordinary annuity FV by (1+r) to convert.

How does compounding frequency affect annuity FV?

More frequent compounding produces a slightly higher FV at the same stated annual rate. Monthly compounding of a 6% APR is equivalent to a 6.17% effective annual rate. For long-horizon retirement savings, this difference adds up to meaningful dollars — a 30-year monthly vs annual comparison can differ by 5-7% in final value.

Is dollar-cost averaging the same as an annuity?

Mathematically yes — regular periodic contributions into an investment is exactly an annuity. DCA into a 401(k), brokerage account, or 529 plan is computed using the FV-of-annuity formula. The variable in real life is the rate of return (which varies year to year); the formula uses an assumed constant return.

How long does $500/month become $1 million?

At 7% annual return (S&P historical real return), $500/month becomes $1 million in approximately 36 years. At 8%, about 33 years. At 5%, about 44 years. The compounding period in the second half of accumulation drives most of the final value — patience is the primary input.

Why is my actual 401(k) growth different from this calculator?

Real markets don't return a constant rate. Sequence of returns matters: a 30% drawdown early in accumulation is fully recoverable; the same drawdown near retirement is much more painful. Use this calculator for planning baselines; use Monte Carlo simulation for risk-aware projections.

Finance

Annuity Future Value Calculator

How much will regular periodic payments be worth in the future with compound interest?

Payment Amount ($)

Interest Rate (%/yr)

Number of Years

Payment Frequency

Type

Formulas:
FV (Ordinary) = PMT × [(1+r)^n − 1] / r
FV (Due) = PMT × [(1+r)^n − 1] / r × (1+r)
Where r = rate per period, n = total periods

The future value of an annuity is the most powerful calculation in personal finance because it captures the magic of regular savings × time × compounding. Most people understand each variable in isolation, but the multiplicative effect when all three combine is the single biggest reason why starting early is dramatically better than catching up later.

The formula and what each piece does

FV_ordinary = PMT × [ ( (1+r)ⁿ − 1 ) / r ]

FV_due = FV_ordinary × (1+r)

PMT: The recurring payment. Scales the result linearly — doubling contributions doubles FV.
r: Periodic rate (annual rate ÷ payments per year). Annual 7% with monthly contributions → r = 0.07/12 = 0.00583.
n: Number of payments (years × frequency). 20 years monthly = 240 payments.
The bracket: FVIFA (Future Value Interest Factor for an Annuity) — the magic compounding multiplier.

$500/month for 20 years at 7%

r = 0.07/12 = 0.005833, n = 240
(1+r)^n = 1.005833^240 ≈ 4.0387
(4.0387 − 1) / 0.005833 = 521.0
FV ordinary = 500 × 521.0 = $260,463
Total contributions = 500 × 240 = $120,000
Compound interest earned: $140,463 — more than the principal contributed

That last bullet is the punchline: in the second half of accumulation, compound growth outpaces new contributions. The $260K total is roughly 54% growth and 46% saved capital.

Ordinary annuity vs annuity due

Same $500/month, 20 years, 7%, but contributions at the beginning of each month:

FV due = 260,463 × 1.005833 = $261,983
Difference: $1,520 — small for monthly compounding, larger for annual.

For an annual annuity due, the difference can be 5-8% of total — meaningful for large balances. Most retirement contributions are ordinary annuities (payments at end of pay period); rent, insurance, and lease payments are annuities due.

Compounding frequency matters less than time

Scenario ($500/mo, 20yr, 7%)	Compounding	FV
Monthly	Monthly	$260,463
Quarterly	Quarterly	$258,977
Annual	Annual	$245,973

Time and rate sensitivity — the punchline

What happens when you change one variable while holding $500/month constant? At 7%:

10 years: $86,542
20 years: $260,463
30 years: $611,729 (more than 2× the 20-year value, with only 50% more contributions)
40 years: $1,313,961 (more than 5× the 20-year value)

The exponential nature means the last decade matters more than all earlier decades combined. This is the single most important reason to start retirement saving in your 20s rather than your 40s.

FAQ

What if the rate is zero?

FV = PMT × n. The formula collapses to simple multiplication, which makes sense intuitively — no compounding, just stacking of payments.

How is this used in 401(k) projections?

HR enrollment tools and brokerage projection screens all run a version of this formula. Inputs: monthly contribution, employer match, expected return, retirement age. Output: projected balance.

Is the FV taxable?

Depends on the account. Traditional 401(k)/IRA: principal and growth taxable on withdrawal. Roth: growth tax-free. Taxable brokerage: only capital gains taxed at sale. The same $260K FV has very different after-tax purchasing power across these vehicles.

How do I adjust for inflation?

Use real return (nominal − inflation) instead of nominal. At 7% nominal and 3% inflation, use 4% real. The same $500/month for 20 years at 4% = $183K in today's dollars — that's the real future purchasing power.

Does the calculator handle changing contributions?

This calculator assumes constant PMT. For escalating contributions (annual raises feeding into 401k), use a growing-annuity formula or year-by-year projection.

What rate of return should I assume?

For long-horizon retirement, financial planners typically use 6-7% nominal (4-5% real). More conservative: 5%. More aggressive: 8% — but be prepared for the variance around the mean.

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Sources

Educational only; not investment or insurance advice. Reviewed by David Roehrig, ChFC®, on March 2, 2026.