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.
FINANCEAn 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%.
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.
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.