Article — Annuity Future Value Calculator
Annuity future value calculator: turn periodic payments into a target balance
The future value of an annuity is the total accumulated value of a series of equal periodic payments at a constant interest rate. The formula is FV = PMT × [((1 + i)^n − 1) ÷ i]. At $500 per month for 30 years earning 6% nominal, the future value is $502,257, of which $322,257 is interest.
Annuity math underlies retirement planning, college savings, mortgage amortization, and bond pricing. The Securities and Exchange Commission cites the same closed-form formula in its investor bulletins on annuities and 401(k) projections. The Internal Revenue Service uses it to value pensions for required minimum distributions.
What is the future value of an annuity?
An annuity is a stream of equal payments at equal intervals. The future value is the sum of those payments compounded forward to a single date. Each payment earns interest on every period after it is made, so earlier payments grow more than later ones. The closed-form formula collapses the sum into one calculation.
The Federal Reserve uses annuity math in its consumer credit modeling. The IRS uses it to compute pension lump sums under Section 415. The Social Security Administration uses it in the actuarial calculations behind benefit projections in Publication 70-10024.
The Roman emperor Domitian issued the first known annuity contracts in the first century AD, promising fixed annual payments in exchange for a lump-sum deposit. The word annuity comes from the Latin annuus, meaning yearly. Britannica traces the modern formula to a 1671 paper by Dutch politician Johan de Witt.
The annuity future value formula
The standard formula has three inputs: the payment amount, the periodic interest rate, and the number of periods. The result depends on whether payments occur at the start or end of each period.
FV (ordinary) = PMT × [((1+i)^n − 1) ÷ i]FV (due) = FV (ordinary) × (1 + i)i (periodic) = annual rate ÷ payments per yearPMT for target = FV ÷ [((1+i)^n − 1) ÷ i]The periodic rate must match the payment frequency. Monthly payments need a monthly rate. Mismatched compounding requires a conversion: convert the annual rate to its effective monthly equivalent using (1 + annual)^(1/12) − 1.
Ordinary annuity vs. annuity due
Ordinary annuities pay at the end of each period. Mortgages, car loans, and bond coupons are ordinary annuities. Annuities due pay at the start. Rent, insurance premiums, and lease payments are annuities due. The IRS distinguishes the two for pension valuation because the timing changes the FV by a factor of (1 + i).
- Ordinary annuity — payments at end of period, lower FV.
- Annuity due — payments at start of period, higher FV by factor (1 + i).
- Perpetuity — ordinary annuity with infinite n, PV = PMT ÷ i, no FV.
- Deferred annuity — payments start after a delay period, common in pension products.
- Growing annuity — payments grow each period at rate g, adjusted formula required.
Picking the discount rate
The rate is the single biggest driver of future value. Federal Reserve H.15 reports 10-year Treasury yields around 4.3% in 2024, the closest thing to a risk-free rate. NYU Stern's Damodaran dataset shows the S&P 500 averaged 10.33% nominal annualized from 1928 through 2024.
Vanguard and Fidelity use 6 to 7% nominal in their retirement projection tools for a balanced 60/40 portfolio. The SEC investor education materials warn against using the long-run S&P 500 average without accounting for sequence-of-returns risk.
Annuity future value examples
A 25-year-old saving $500 per month at 7% nominal until age 65 reaches $1,197,838 by retirement, of which contributions are $240,000 and interest is $957,838. The same monthly payment from age 35 reaches $566,764, less than half. The 10-year head start adds $645,524 from compounding alone.
The 401(k) employee contribution limit in 2024 is $23,000 ($30,500 if age 50+). Maxed out at 7% nominal over a 40-year career, that produces an annuity FV of $4.59 million on $920,000 in contributions.
Inflation and real FV
The annuity formula produces a nominal FV. The real purchasing power depends on inflation over the same period. The Bureau of Labor Statistics has measured average CPI inflation of 3.04% since 1928. The Federal Reserve targets 2% going forward.
At 2% inflation, $1 million in 30 years has the purchasing power of $552,071 today. At 3% inflation, the same nominal $1 million is worth only $411,987 in today's dollars. Always compare retirement targets in real terms.
Common annuity mistakes
The most common mistake is mismatching the rate and the period. A 6% annual rate becomes 0.5% per month, not 6% per month. The second is confusing ordinary annuity with annuity due. The third is using a long-run historic rate without adjusting for inflation.
- Rate-period mismatch — divide annual rate by payments per year.
- Ordinary vs. due confusion — rent (due) and mortgage (ordinary) use different formulas.
- Nominal-vs-real conflation — FV is nominal, divide by (1 + inflation)^years for real.
- Ignoring sequence risk — the closed-form formula assumes constant returns; real markets cluster losses.
- Forgetting tax wrapper — 401(k) and IRA grow tax-deferred; taxable brokerage drags returns by 0.5-1.5% per year.
Annuity future value vs. present value
Future value tells you what a stream of payments will be worth at a future date. Present value tells you what those payments are worth today. They are two sides of the same formula. PV of an annuity is FV divided by (1 + i)^n. The SEC's investor education site uses both interchangeably depending on the question.
Use FV when planning toward a target (retirement, college). Use PV when evaluating a lump-sum offer (pension buyout, lottery payout) against a stream of payments. The IRS Section 415 actuarial tables use PV to convert pensions to lump sums, applying the segment rates published monthly by the Treasury Department.
The relationship between PV and FV is symmetric. For the same payment stream and interest rate, FV at time n equals PV multiplied by (1 + i)^n. A series of 240 monthly $500 payments at 6% has a PV of $69,790 today and an FV of $231,020 in 20 years. The two numbers describe the same annuity from different vantage points. The CFA Institute curriculum and the SEC investor bulletins both teach FV and PV as inverse operations on the same time line.