What is an annuity (the math) vs an annuity (the insurance product)?

The MATH of an annuity is just a series of equal periodic payments — present value, future value, and payment solving are pure actuarial calculations. The PRODUCT 'annuity' is a financial instrument (typically sold by insurance companies) that promises a stream of payments in exchange for a lump sum or premium series. The math is universal; the product wraps it in fees, surrender charges, and guarantees. This calculator does the math without the product overhead.

What's the formula for future value of an annuity?

FV = PMT × [(1+r)^n − 1] / r — where PMT is the periodic payment, r is the periodic rate, and n is number of periods. This assumes payments at the END of each period (ordinary annuity). For payments at the start of each period (annuity due), multiply by (1+r). The calculator uses ordinary-annuity convention as the standard.

What's the formula for present value of an annuity?

PV = PMT × [1 − (1+r)^−n] / r — the discounted value of a future payment stream at today's value. PV grows with PMT and n, shrinks with r. At r=0, PV = PMT × n (simple sum). High discount rates aggressively reduce PV (the further-out payments contribute less today).

How do I use the 'PMT from a pool' mode?

It answers 'I have $X today; how much can I withdraw per year for N years at rate r before depleting?' Formula: PMT = PV × r / [1 − (1+r)^−n]. At $1M / 30 years / 4%, that's about $58K/year. At 5% it's $65K. The mode treats the pool like an immediate-pay annuity — the standard retirement-withdrawal math.

What's a realistic rate of return to use?

Conservative: 3–4% (inflation-protected bonds, money market). Balanced: 5–6% (60/40 portfolio long-run real return). Aggressive: 7–8% (mostly stocks). Don't use stock-market nominal returns (~10%) without subtracting inflation — for retirement planning, use REAL (inflation-adjusted) returns of 4–6%. Higher rates produce optimistic results that disappoint in actual experience.

Are annuity payments taxable?

Yes, but depending on type. Qualified annuities (in IRA/401k): fully taxable as ordinary income at withdrawal. Non-qualified annuities (purchased with after-tax dollars): only the gains portion is taxable; the original investment (basis) is returned tax-free over time per IRS exclusion ratio. Pensions are typically fully taxable. The math here is pre-tax; multiply by (1 − marginal rate) for after-tax dollars.

What's the difference between fixed and variable annuities (the product)?

Fixed: insurance company guarantees a specific rate (typically 3–5% in 2026). Variable: returns depend on underlying investment sub-accounts (mutual-fund-like). Indexed: returns linked to an index (S&P 500) with caps and floors. Fixed has lowest variability; variable has highest risk + reward; indexed is the middle. The math calculator here is rate-agnostic — plug in whatever realistic return you want.

When are annuity products worth buying?

Limited cases. (1) Longevity insurance: deferred-income annuity bought at 65 paying starting at 80 — protects against outliving savings. (2) Pension-replacement: lifetime income for people without traditional pensions. (3) High-net-worth tax-deferral above 401k/IRA caps. AVOID: high-commission variable + indexed annuities sold by salespeople. They typically charge 2–3.5% annual fees that destroy the math. Direct-purchased income annuities from low-cost providers (Vanguard, Fidelity) have lower fees.

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

Ordinary annuity: payments at the END of each period (most common). Annuity due: payments at the BEGINNING. The math is identical except annuity-due values are (1+r) times ordinary-annuity values. The calculator assumes ordinary. For monthly rent or annual property tax (paid in advance), use annuity-due; for typical bond coupons or retirement-account withdrawals, ordinary is correct.

How does inflation affect annuity math?

Critical. A $50K/year annuity payment for 30 years sounds great today but loses ~50% of purchasing power at 3% inflation. To preserve purchasing power, either: (1) buy an inflation-adjusted annuity (TIPS-based or CPI-linked — pays more upfront with a smaller initial payment but adjusts), or (2) use REAL (inflation-adjusted) return rates in the calculator (subtract expected inflation from nominal rate). Fixed nominal annuities erode dramatically over long periods.

What's the 4% rule and how does it relate to annuity math?

The Trinity Study '4% rule' says retirees withdrawing 4% of initial portfolio (inflation-adjusted) annually have ~95% chance of not depleting over 30 years (in historical US data). At $1M, that's $40K/year. Annuity math says PMT from a $1M pool at 4% real return over 30 years is ~$57K/year — but that assumes you DEPLETE the principal. The 4% rule preserves principal probabilistically; annuity math gives you the higher 'spend it all' number.

Can I use this calculator for monthly annuities?

Yes, with conversion. The calculator uses annual conventions, so for monthly math: enter annual rate ÷ 12 as 'rate', enter months as 'periods', and your monthly payment as 'payment'. The result is your monthly FV or PV. Just keep the units consistent within a calculation.

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Annuity Calculator — PV / FV / Payment 4-Way Solve

Drop your inputs and pick what to solve for — future value of payments, present value of an income stream, periodic payment from a pool, or payment required to hit a target FV. Standard actuarial math; no fee-bearing annuity-product distortion.

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Reviewed by CalcBold Editorial · Sources: IRS Pub 575 (annuity taxation) + Society of Actuaries primers + Trinity Study (Bengen 1994 + 1998 updates)Last verified May 15, 2026Methodology

Solve for

Pick what you're solving for. The other three inputs scale to the chosen mode.

Initial deposit / lump sum (PV)

For 'PMT from a pool', this is the pool. For 'FV of payments', a separate starting balance that also grows.

Periodic payment

Annual payment in or out. For 'FV/PV of payments' this is the stream amount.

Years

Annual periods. For monthly annuities, multiply rate÷12 and use months for periods (this calculator uses annual conventions).

Rate (% per year)

Discount rate for PV; expected growth rate for FV. Use realistic real return (3–6% for diversified portfolios, ~5% baseline).

Target FV (for PMT-to-FV mode)

Only used when solving for the payment needed to hit a target. Ignored for other modes.

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What is an Annuity?

An annuity is a financial contract — typically issued by an insurance company — that pays out a series of payments over time. You hand the issuer a lump sum (or build the balance through contributions), and in exchange the issuer guarantees you a stream of future income, either for a fixed number of years or for the rest of your life. Annuities are the primary instrument for converting a retirement nest-egg into guaranteed income.

Three big variants get conflated in everyday speech:

Fixed annuity — guaranteed payout amount, locked at contract signing. Issuer takes the investment risk.
Variable annuity — payout floats with underlying investment performance (usually mutual-fund sub-accounts). You take the investment risk.
Indexed annuity— payout tied to a market index (S&P 500) with a floor and a cap. Hybrid of fixed and variable.

This calculator handles the math of all three: enter the principal, expected return rate, payout duration, and payout timing — it computes the periodic payment, total paid out, and effective rate of return.

Two Common Calculations

Most annuity questions reduce to one of two scenarios:

Accumulation phase (saving)— you contribute monthly until retirement. The calculator answers “what balance will I have?” Mathematically equivalent to the future-value-of-an-annuity formula in any compound-interest calculator.
Payout phase (spending)— you have a fixed balance and want a guaranteed monthly income over X years (or for life). The calculator answers “what monthly payment can I draw?” Mathematically equivalent to the present-value-of-an-annuity formula.

Pick the phase that matches your question. The calculator routes the math accordingly.

When to Use This Calculator vs the Siblings

Use this generic annuity calculator when you’re evaluating an annuity you would buy — typically a deferred fixed annuity from an insurance carrier, or a SPIA (single-premium immediate annuity) at retirement. Use the Pension Lump-Sum vs Annuity calculator when an employer is offering you a buyout of an old defined-benefit plan, and the Powerball Annuity Calculator when you’ve won a multi-state lottery and need to choose between cash and the 29-year graduated annuity option.

Related Tools

For the accumulation side (saving toward retirement), the compound interest calculator is the right tool — same future-value-of-an-annuity formula, just unwrapped from the insurance product. For the spending side (drawing from a retirement balance), the retirement savings calculator models the 4% safe-withdrawal heuristic without requiring an insurance company in the middle. And for the RMD-driven required draws from tax-deferred accounts after age 73, use the RMD calculator.

Frequently Asked Questions

The most common questions we get about this calculator — each answer is kept under 60 words so you can scan.

What is an annuity (the math) vs an annuity (the insurance product)?
The MATH of an annuity is just a series of equal periodic payments — present value, future value, and payment solving are pure actuarial calculations. The PRODUCT 'annuity' is a financial instrument (typically sold by insurance companies) that promises a stream of payments in exchange for a lump sum or premium series. The math is universal; the product wraps it in fees, surrender charges, and guarantees. This calculator does the math without the product overhead.
What's the formula for future value of an annuity?
FV = PMT × [(1+r)^n − 1] / r — where PMT is the periodic payment, r is the periodic rate, and n is number of periods. This assumes payments at the END of each period (ordinary annuity). For payments at the start of each period (annuity due), multiply by (1+r). The calculator uses ordinary-annuity convention as the standard.
What's the formula for present value of an annuity?
PV = PMT × [1 − (1+r)^−n] / r — the discounted value of a future payment stream at today's value. PV grows with PMT and n, shrinks with r. At r=0, PV = PMT × n (simple sum). High discount rates aggressively reduce PV (the further-out payments contribute less today).
How do I use the 'PMT from a pool' mode?
It answers 'I have $X today; how much can I withdraw per year for N years at rate r before depleting?' Formula: PMT = PV × r / [1 − (1+r)^−n]. At $1M / 30 years / 4%, that's about $58K/year. At 5% it's $65K. The mode treats the pool like an immediate-pay annuity — the standard retirement-withdrawal math.
What's a realistic rate of return to use?
Conservative: 3–4% (inflation-protected bonds, money market). Balanced: 5–6% (60/40 portfolio long-run real return). Aggressive: 7–8% (mostly stocks). Don't use stock-market nominal returns (~10%) without subtracting inflation — for retirement planning, use REAL (inflation-adjusted) returns of 4–6%. Higher rates produce optimistic results that disappoint in actual experience.
Are annuity payments taxable?
Yes, but depending on type. Qualified annuities (in IRA/401k): fully taxable as ordinary income at withdrawal. Non-qualified annuities (purchased with after-tax dollars): only the gains portion is taxable; the original investment (basis) is returned tax-free over time per IRS exclusion ratio. Pensions are typically fully taxable. The math here is pre-tax; multiply by (1 − marginal rate) for after-tax dollars.
What's the difference between fixed and variable annuities (the product)?
Fixed: insurance company guarantees a specific rate (typically 3–5% in 2026). Variable: returns depend on underlying investment sub-accounts (mutual-fund-like). Indexed: returns linked to an index (S&P 500) with caps and floors. Fixed has lowest variability; variable has highest risk + reward; indexed is the middle. The math calculator here is rate-agnostic — plug in whatever realistic return you want.
When are annuity products worth buying?
Limited cases. (1) Longevity insurance: deferred-income annuity bought at 65 paying starting at 80 — protects against outliving savings. (2) Pension-replacement: lifetime income for people without traditional pensions. (3) High-net-worth tax-deferral above 401k/IRA caps. AVOID: high-commission variable + indexed annuities sold by salespeople. They typically charge 2–3.5% annual fees that destroy the math. Direct-purchased income annuities from low-cost providers (Vanguard, Fidelity) have lower fees.
What's the difference between annuity due and ordinary annuity?
Ordinary annuity: payments at the END of each period (most common). Annuity due: payments at the BEGINNING. The math is identical except annuity-due values are (1+r) times ordinary-annuity values. The calculator assumes ordinary. For monthly rent or annual property tax (paid in advance), use annuity-due; for typical bond coupons or retirement-account withdrawals, ordinary is correct.
How does inflation affect annuity math?
Critical. A $50K/year annuity payment for 30 years sounds great today but loses ~50% of purchasing power at 3% inflation. To preserve purchasing power, either: (1) buy an inflation-adjusted annuity (TIPS-based or CPI-linked — pays more upfront with a smaller initial payment but adjusts), or (2) use REAL (inflation-adjusted) return rates in the calculator (subtract expected inflation from nominal rate). Fixed nominal annuities erode dramatically over long periods.
What's the 4% rule and how does it relate to annuity math?
The Trinity Study '4% rule' says retirees withdrawing 4% of initial portfolio (inflation-adjusted) annually have ~95% chance of not depleting over 30 years (in historical US data). At $1M, that's $40K/year. Annuity math says PMT from a $1M pool at 4% real return over 30 years is ~$57K/year — but that assumes you DEPLETE the principal. The 4% rule preserves principal probabilistically; annuity math gives you the higher 'spend it all' number.
Can I use this calculator for monthly annuities?
Yes, with conversion. The calculator uses annual conventions, so for monthly math: enter annual rate ÷ 12 as 'rate', enter months as 'periods', and your monthly payment as 'payment'. The result is your monthly FV or PV. Just keep the units consistent within a calculation.