Annuity Calculator

In financial mathematics an annuity is a series of equal payments made at regular intervals over a fixed term. Examples include monthly mortgage repayments, pension payouts, insurance premiums and systematic withdrawal plans. The two key questions an annuity calculator answers are: 'what lump sum today is equivalent to receiving these payments?' (present value) and 'what will these payments grow to by the end of the term?' (future value).

Present value (PV) is the lump sum you would need to invest today at the given rate to reproduce the same payment stream — it discounts the payments back to today. Future value (FV) is the total amount accumulated if every payment is reinvested at the given rate until the end of the term. Use PV when you want to know what a stream of future payouts is worth today; use FV when you want to know how much a series of deposits will grow to.

An ordinary annuity (also called annuity-immediate) makes each payment at the END of the period. An annuity due makes each payment at the START of the period. Because each payment in an annuity due is one period earlier, every payment earns one extra period of interest, so both the PV and FV of an annuity due are exactly (1 + r) times those of the equivalent ordinary annuity. Most loan payments are ordinary annuities; some savings or leasing contracts are set up as annuities due.

For an ordinary annuity: PV = PMT × [1 − (1 + r)^−n] / r, where PMT is the payment per period, r is the interest rate per period (annual rate ÷ payments per year), and n is the total number of periods (years × payments per year). For an annuity due, multiply the result by (1 + r). At a zero rate the formula reduces to PV = PMT × n.

For an ordinary annuity: FV = PMT × [((1 + r)^n − 1) / r], where PMT is the payment per period, r is the rate per period, and n is the total number of periods. For an annuity due, multiply by (1 + r). At a zero rate FV = PMT × n.

Payment frequency sets both how often payments are made and how often interest compounds (the calculator assumes they match). More frequent payments at the same annual rate mean each payment earns interest sooner, so the FV is slightly higher and the PV is slightly lower compared with the same total annual amount paid annually. For example, $1,000/month is not the same as $12,000/year when rates are non-zero, because the monthly version starts earning interest earlier.

At 0% no compounding occurs, so PV = FV = PMT × n — just the sum of all payments with no interest. The textbook formulas produce a 0/0 indeterminate form at zero rate, which is why a correct calculator evaluates the limit (which is n) rather than dividing by zero. At 0% the ordinary annuity and annuity due produce exactly the same result.

The Future Value Calculator on this site is designed to project a starting lump sum plus optional regular contributions forward in time — present value is an INPUT (the amount you have today). This Annuity Calculator treats the regular PAYMENT as the primary input and solves in both directions: it can compute either the present value (lump-sum equivalent today) or the future value (accumulated total at maturity) of a payment stream. Use the Annuity Calculator when you know the payment and want either the PV or FV; use the Future Value Calculator when you know an initial lump sum you want to grow.

Yes, as an illustrative estimate. Enter the regular payment, the discount/interest rate, the term and the payment frequency. The result is a textbook time-value-of-money calculation. However, real insurance annuities include mortality credits, fees, guarantee provisions and insurer-specific rates that can make the actual value differ from this figure. Treat the result as educational guidance, not a product quote.

The discount rate should reflect the opportunity cost of the money — what you could earn in an alternative investment of similar risk. For a government-backed pension, a low risk-free rate (e.g. current government bond yield) is reasonable. For a corporate annuity or insurance product, you might use a rate that reflects the creditworthiness of the payer. There is no universally 'correct' rate; the calculator lets you explore different scenarios by changing the rate.

Mortgage payments follow the same ordinary-annuity PV formula — the loan amount is the present value and you solve for the payment. This calculator works in the other direction: given a payment, it tells you the equivalent present value. To find the payment that amortises a specific loan amount, the EMI Calculator or Amortization Calculator on this site are purpose-built for that.

Textbooks often round intermediate values (such as the annuity factor) to a set number of decimal places before multiplying, which shifts the final result by a cent or two. This calculator rounds only once at the very end, which is the more precise approach. For example, OpenStax quotes $99,817.81 for the 25,000/year, 5-year, 8% example, while this calculator computes $99,817.75 — the 6-cent gap is entirely due to intermediate rounding in the textbook.

No. All results are gross nominal amounts before inflation and taxes. Inflation erodes the real purchasing power of future payments, so the real present value is lower than shown if you expect significant inflation over the term. For after-tax or inflation-adjusted analysis, consult a financial adviser.

An immediate annuity begins paying out straight away — usually within a month of purchase. A deferred annuity has an accumulation phase first: premiums are invested and grow over time, and payouts only begin at a future date (such as retirement). This calculator models the time-value-of-money arithmetic common to both types; it does not model the accumulation phase of a deferred product separately.

A fixed annuity pays a guaranteed interest rate set by the insurer, so your payment amount is predictable. A variable annuity invests in sub-accounts (similar to mutual funds), so the payout depends on market performance and is not guaranteed. An equity-indexed annuity links returns to a stock-market index (such as the S&P 500) with a floor that limits losses and a cap that limits gains. This calculator assumes a fixed rate throughout the term, which matches the fixed-annuity model; variable and equity-indexed products require scenario analysis beyond a single rate.

A growing annuity is like an ordinary annuity except that each payment increases by a constant growth rate g each period (for example, a pension that rises 2% a year to keep pace with inflation). The future-value formula becomes FV = PMT × ((1 + r)^n − (1 + g)^n) / (r − g) when r ≠ g, and PV has an analogous adjustment. This calculator models a level (flat) payment stream; if you need a growing-payment model, treat this tool's result as a baseline and consult a financial adviser or a purpose-built growing-annuity tool for the growth-adjusted figure.