An annuity converts a lump sum of money into a guaranteed stream of periodic payments, making it a cornerstone of retirement income planning, pension calculations, and structured settlement valuations. The mathematics behind annuities — present value, future value, and payment calculations — apply to any regular cash flow series including mortgage payments, lease agreements, and insurance payouts. The present value of an ordinary annuity (PV = PMT × [(1 - (1+r)^-n) / r]) determines how much a series of future payments is worth today, while the future value formula shows how regular contributions grow with compound interest. Our annuity calculator handles both scenarios: enter a lump sum to find the periodic payment it will generate, or enter desired payments to find the required principal. It supports immediate and deferred annuities, fixed and variable rates, and different payment frequencies — monthly, quarterly, or annually — giving you a complete picture of how annuities fit into your financial plan.
Annuity math in one page
An annuity is simply a stream of equal payments at equal intervals. The two building-block formulas are: PV = PMT × (1 − (1+r)^-n) / r and FV = PMT × ((1+r)^n − 1) / r. Both assume payments at the end of each period (ordinary annuity). If payments happen at the beginning (annuity due), each payment gets one extra period of compounding or discounting, so multiply both PV and FV by (1+r). To solve for PMT, algebraically invert: PMT = PV × r / (1 − (1+r)^-n) for a given PV, or PMT = FV × r / ((1+r)^n − 1) for a given FV. This calculator always applies the (1+r) factor automatically when you pick 'annuity due'.
When to use each mode
Use PRESENT VALUE when you know the payment stream and want today's lump-sum equivalent — pricing a bond coupon strip, valuing a pension, or figuring out how much principal backs a mortgage payment. Use FUTURE VALUE when you want to know what a regular contribution grows to — a sinking fund, a savings plan, or an annuity's accumulated balance at retirement. Use PAYMENT when you have a target (mortgage principal, retirement nest egg, bond face value) and want the equal payment that hits it — this is the same math as a loan amortization schedule.