How this works
An annuity is a series of equal cash flows occurring at regular intervals — every month, every quarter, every year — over a defined number of periods. Pensions, mortgages, leases, retirement contributions, and bond coupons are all annuities under the hood. The calculator solves the same equation three ways depending on which two of {present value, future value, payment} you know.
Two timing conventions matter. (1) Ordinary annuity: the payment lands at the END of each period. Most loans, retirement income, and bond coupons follow this convention. (2) Annuity due: the payment lands at the START of each period. Rent, leases, and many insurance premiums work this way. The mathematical difference is one extra period of compounding for an annuity due, so its future value is higher by a factor of (1 + r) and its present value is also higher by the same factor.
Be careful with rate and frequency. If the stated rate is 6% APR and you contribute monthly, the per-period rate is 6%/12 = 0.5% and the number of periods is years × 12. Most spreadsheet errors trace back to mismatching the two — using an annual rate with a monthly period count will produce wildly wrong numbers. This calculator handles the conversion for you, but if you are checking with a hand formula, line them up.
The formula
PMT is the periodic payment (deposit or withdrawal). r is the per-period rate. n is the total number of periods. FV is the value at the end. PV is the value today. (1 + r) factor on annuity-due reflects one extra compounding period because each payment is made one period earlier.
Example calculation
- $500/month, 6% APR, 30 years, ordinary annuity (end of month).
- r = 0.06/12 = 0.005, n = 360. FV = 500 × ((1.005^360 − 1)/0.005) ≈ $502,257.
Frequently asked questions
When should I use annuity due instead of ordinary?
Match the cash-flow timing of the contract. Rent and most leases pay at the start of the month → annuity due. Loan repayments, retirement income, and bond coupons pay at the end → ordinary. Picking the wrong one shifts every result by one (1 + r) factor — small per-period, but it compounds over decades. If unsure, look at the contract: which day of the month does money move?
Why does the result not match my bank's figure?
Common causes: (1) rate is APR but bank uses APY (or vice versa) — APY = (1 + APR/n)^n − 1 with continuous-style compounding. (2) Bank charges fees that show up in the net result but not the textbook formula. (3) First period is partial (account opened mid-month). (4) Day-count convention (30/360 vs actual/365) differs. For exact matching, ask the bank for their day-count and APR-vs-APY definitions.
Can I use this for a 401(k) or IRA?
Yes — this is the underlying maths for a flat-payment retirement vehicle. Use monthly frequency, your contribution as PMT, your expected long-run return as the rate, and years to retirement as the term. Solve for FV. Two caveats: (1) you should subtract investment fees from the rate (a 1% expense ratio on a 6% gross return → use 5%), and (2) actual returns are volatile, so the FV is a single-point estimate. For risk planning, also try a low/high scenario.