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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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.

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