Annuity Calculator
Calculate the present value and future value of ordinary annuities and annuities-due. Find payment amounts, interest rates, or number of periods.
What Is the Annuity Calculator?
An annuity is a series of equal payments made at regular intervals. The present value (PV) of an annuity is what that stream of future payments is worth today; the future value (FV) is how much the stream will accumulate to. Ordinary annuities pay at the end of each period; annuities-due pay at the beginning. This calculator handles both types, as well as solving for the payment amount given a target PV or FV.
Formula
How to Use
Choose whether you want Present Value (PV) or Future Value (FV). Enter the periodic payment, annual interest rate, number of periods (and compounding frequency), and the annuity type. The calculator outputs the PV or FV, total payments, and total interest earned or paid.
Example Calculation
You invest $500/month for 20 years at 6% annual rate (monthly compounding): FV = 500 × [(1+0.005)^240 − 1] / 0.005 ≈ $231,020. Total contributions: $120,000. Interest earned: $111,020.
Understanding Annuity
Annuity mathematics forms the backbone of financial planning, insurance pricing, and fixed-income investing. The present value formula discounts each future payment back to today using the interest rate as the discount factor, then sums them. Because payments are equal, this simplifies to the compact closed-form formula shown above.
The future value formula compounds each payment forward to the end of the annuity's life. A small difference in interest rate has a compounding effect that grows dramatically over longer time horizons — illustrating why starting retirement savings early is mathematically powerful.
Perpetities — annuities that pay forever — have PV = PMT / r. This formula is used to value stocks via the Gordon Growth Model and to price consol bonds.
Real-world annuities include mortgage payments (PV calculation), car loans, pension income streams, lottery structured settlements, and systematic investment plans (SIP). Understanding PV and FV empowers consumers to compare financial products accurately rather than relying solely on advertised rates.
Frequently Asked Questions
What is the difference between an ordinary annuity and an annuity-due?
An ordinary annuity (most common) makes payments at the end of each period — like most loan repayments and retirement distributions. An annuity-due makes payments at the start of each period — like rent or insurance premiums. Annuity-due values are always slightly higher.
What is the present value of an annuity used for?
PV is used to determine how much a stream of future payments is worth today, accounting for the time value of money. Lenders use it to price loans; investors use it to value bonds and dividend streams; pension actuaries use it to fund retirement liabilities.
What is the future value of an annuity used for?
FV tells you how much your regular savings or investments will grow to. It is the core formula behind retirement savings projections, education fund planning, and any goal-based saving scenario.
How do I solve for the payment amount instead?
Use the PMT solve option. Enter your target PV or FV, rate, and number of periods, and the calculator back-solves for the required payment. This is useful for working out how much to save each month to reach a goal.