Annuity Calculator - Payment and Present/Future Value

What Is an Annuity? An annuity is a series of equal payments made at regular intervals over a defined period. The word comes from the Latin “annus” (year), reflecting the original use for annual pension payments. Today, annuities describe any regular payment stream: monthly mortgage payments, quarterly bond coupon payments, or annual insurance premiums.

Ordinary Annuity vs. Annuity Due An ordinary annuity (also called an annuity-in-arrears) makes payments at the END of each period. This is the most common type: mortgages, car loans, most savings plans, and corporate bond coupons are all ordinary annuities. An annuity due makes payments at the BEGINNING of each period, which is how rent, insurance premiums, and some leases work. Because payments arrive one period earlier, they have slightly more time to compound, making the annuity due worth slightly more.

Present Value of an Annuity The present value (PV) tells you what a future stream of payments is worth today. This requires a discount rate, which is the opportunity cost of money. A lottery winner choosing between $1 million today or $70,000/year for 20 years must calculate the PV of the annuity at some discount rate. At a 5% discount rate, the 20-year annuity has a PV of only $872,000, less than the lump sum. At 3%, the PV rises to $1,041,000, more than the lump sum. The discount rate assumption changes everything.

Future Value of an Annuity The future value (FV) answers: if I save a fixed amount each period, how much will I have after n periods? This is the core calculation for retirement savings. Saving $500/month at a 7% annual return, compounded monthly, for 30 years grows to $609,985. You only contributed $180,000 of that. The other $429,985 is compound interest.

Watch what a decade does. Run the same $500/month for 40 years instead of 30 and you finish with $1,312,407, not the $813,000 you might expect from adding a third more time. The last ten years earn more than the first twenty combined.

The Pension and Insurance Industry Insurance companies use annuity math extensively to price products. A life annuity pays income for as long as you live, so the insurer must calculate the expected present value of all future payments, discounted and probability-weighted by survival rates from actuarial life tables.

Inflation Warning Fixed annuity payments have a real enemy: inflation. US consumer prices roughly doubled between 1994 and 2024, so a $2,000/month pension fixed in 1994 buys about what $950 bought back then. The pensioner still receives $2,000. Many pension and Social Security benefits include cost-of-living adjustments (COLAs) to address this. When evaluating any fixed payment stream, always consider its inflation-adjusted value.