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Annuity Calculator (Present & Future Value)

Calculate PV, FV, or payment of an annuity. Handles ordinary vs annuity-due and annual, quarterly, or monthly compounding with year-by-year accumulation table.

FINANCE

An annuity is a stream of equal cash flows at regular intervals - rent, mortgage payments, bond coupons, 401(k) contributions, and insurance-product annuities all fit the pattern. This calculator collapses the stream into a single number (present value or future value) or solves for the payment needed to hit a target.

Pick what you want to solve for (PV, FV, or PMT), supply the other inputs, choose payment frequency, and choose whether payments occur at the end of each period (ordinary annuity) or the start (annuity-due). The math: with periodic rate r = annual_rate / freq and total periods n = years × freq, the ordinary annuity formulas are PV = PMT × (1 - (1+r)^-n) / r and FV = PMT × ((1+r)^n - 1) / r; for an annuity-due, multiply by (1+r). To solve for PMT, invert the relevant formula. Worked example: PMT $500/month for 20 years at 5% annual, monthly compounding, ordinary annuity gives FV approximately $205,517 and PV approximately $75,755. Switching to annuity-due raises each result by a factor of (1 + 0.05/12) - roughly 0.42%.

Disclaimer: Education only. Retail annuities sold by insurance companies have surrender charges, mortality and expense fees, rider costs, and tax treatment that this calculator does not model. Read the contract and compare quotes before buying any insurance product.

Annuity Calculator (Present & Future Value)

Solve for the present value, future value, or periodic payment of an annuity. Supports ordinary annuities (payments at period end) and annuities-due (payments at period start) with annual, quarterly, or monthly compounding.

Solve For

Present Value (PV)Future Value (FV)Payment (PMT)

Periodic Payment ($)The equal cash flow paid each period.

Annual Interest Rate (%)Nominal annual rate. Will be divided by payment frequency.

Number of Years

Payment Frequency

AnnualQuarterlyMonthly

Annuity Type

Ordinary (end of period)Annuity-Due (start of period)

Future Value

$205,517

Present Value$75,763

Periodic Payment$500.00

Total Contributions$120,000

Total Interest$85,517

Total Periods240

Year-by-Year Accumulation

Year	Contributions	Interest Earned	Balance
1	$6,000	$139	$6,139
2	$6,000	$454	$12,593
3	$6,000	$784	$19,377
4	$6,000	$1,131	$26,507
5	$6,000	$1,496	$34,003
6	$6,000	$1,879	$41,882
7	$6,000	$2,282	$50,164
8	$6,000	$2,706	$58,870
9	$6,000	$3,151	$68,022
10	$6,000	$3,620	$77,641
11	$6,000	$4,112	$87,753
12	$6,000	$4,629	$98,382
13	$6,000	$5,173	$109,555
14	$6,000	$5,744	$121,299
15	$6,000	$6,345	$133,644
16	$6,000	$6,977	$146,621
17	$6,000	$7,641	$160,262
18	$6,000	$8,339	$174,601
19	$6,000	$9,072	$189,673
20	$6,000	$9,843	$205,517

About Annuities

In finance theory, an annuity is simply a stream of equal cash flows occurring at regular intervals — your monthly rent, a bond coupon, a 401(k) contribution, or a mortgage payment all qualify. The math lets you collapse that stream into a single number, either its value today (present value) or its accumulated value at the end (future value). In US retail finance, the word "annuity" also refers to an insurance product (fixed, indexed, or variable) that pays out a stream of income, often in retirement — same underlying math, but wrapped in a contract with fees and guarantees.

Ordinary annuity vs. annuity-due is just a timing distinction. In an ordinary annuity, each payment occurs at the END of the period — bond coupons, mortgage payments, and most loan payments work this way. In an annuity-due, each payment occurs at the START of the period — rent, insurance premiums, and lease payments typically work this way. Because annuity-due payments sit in the account one extra period earning interest, both PV and FV of an annuity-due equal the ordinary version multiplied by (1 + r).

Real-world US examples: a single-premium immediate annuity (SPIA) from an insurer converts a lump sum into a lifetime monthly check — useful for retirement income. A Powerball "annuity" prize is paid over 30 years; the lump-sum option is the present value of that stream at the lottery's assumed discount rate (typically much smaller than the advertised jackpot). Your mortgage is an annuity from the bank's point of view: they paid PV today (the loan amount) and collect PMT every month for n months, with the rate baked in.

For education only. Retail annuities sold by insurance companies have surrender charges, mortality and expense fees, rider costs, and tax treatment that this calculator does not model. Always read the contract and compare quotes before purchasing.

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Frequently Asked Questions

What is an annuity in finance?

In finance theory, an annuity is any stream of equal cash flows occurring at regular intervals - your rent, a bond's coupon payments, a mortgage payment, or systematic 401(k) contributions all qualify. The math lets you express that stream as a single present value (worth today) or future value (accumulated at the end). The same word is also used in US retail finance for an insurance product that pays a stream of income, often in retirement.

What is the difference between ordinary annuity and annuity-due?

It is purely a timing distinction. In an ordinary annuity each payment occurs at the END of the period - bond coupons and most loan payments work this way. In an annuity-due each payment occurs at the START of the period - rent, leases, and insurance premiums typically work this way. Because annuity-due payments sit one extra period earning interest, both PV and FV equal the ordinary version multiplied by (1 + r).

How do I solve for the payment given a target future value?

Set the calculator's mode to PMT and enter your target FV (and years, rate, frequency). The formula is PMT = FV × r / ((1+r)^n - 1) for an ordinary annuity, or divided by an additional (1+r) factor for annuity-due. Example: to accumulate $1,000,000 in 30 years at 7% annual, monthly compounding, ordinary, you need about $820 per month.

Is a retail annuity (from an insurance company) the same thing?

The underlying time-value math is the same, but a retail annuity is a contract wrapped around it. Fixed, indexed, and variable annuities add features like lifetime income guarantees, death benefits, and tax deferral, but they also charge mortality and expense fees, rider fees, and surrender charges that can be substantial. Always compare net-of-fees yield against simpler alternatives like a bond ladder or TIPS.

Should I take the lottery as a lump sum or annuity?

It depends on the implied discount rate. The lottery's lump-sum option is roughly the present value of the 30-year payment stream at the lottery's assumed rate, after withholding. If you can reliably earn more than that rate net of tax (often a high bar), the lump sum wins. If you cannot - or you are worried about spending discipline - the annuity option is structurally safer because it spreads income and tax across decades.

Annuity Calculator (Present & Future Value)

Annuity Calculator (Present & Future Value)

Year-by-Year Accumulation

About Annuities

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