Calculate annuity present value, future value, and periodic payment amounts.
Formulas: FV = PMT × [(1+r)^n − 1] / r PV = PMT × [1 − (1+r)^−n] / r Annuity Due: multiply by (1+r)
An annuity is any series of equal periodic payments — the building block of nearly all personal-finance math. This calculator handles the three standard questions: how much will I have (FV), how much is this worth today (PV), and how much do I need to pay (PMT). Internally they're the same formula rearranged for a different unknown.
The three time-value-of-money questions
FV (Future Value) — accumulation. Use for retirement savings, education funding, and any forward-looking "what will my contributions grow to" question.
PV (Present Value) — discounting. Use for valuing pensions, lottery payouts, structured settlements, and any "what is this future stream worth today" question.
PMT (Payment) — solving for the contribution required. Use for "I want $1 million in 30 years — how much per month?" or "I want to amortize a $200K liability over 15 years — what does it cost monthly?"
Three quick examples
FV: $500/month, 6% annual, 20 years monthly compounding → FV ≈ $231,020. Total contributions $120,000; growth $111,020.
PV: $1,000/month for 10 years at 6% → PV ≈ $90,073. Total future cash $120,000; discount $29,927.
PMT: Save $1M in 25 years at 7% → required monthly contribution ≈ $1,251.
Ordinary vs annuity due — the (1+r) detail
End-of-period payments are "ordinary." Beginning-of-period payments are "annuity due." Most savings/loans are ordinary; rent and insurance premiums are due. Convert by multiplying by (1+r). Over short horizons the difference is small; over 30+ year retirement horizons it can equal a year's contribution.
Variants worth knowing
Perpetuity: Infinite-life annuity. PV = PMT / r. Used for preferred stock valuation.
Growing annuity: Payments grow at constant g. Models inflation-indexed pensions and contribution escalation.
Deferred annuity: Payments don't start until a future date. PV = PV of ordinary annuity ÷ (1+r)defer.
Variable annuity: Commercial product where payouts vary with underlying investment returns. Requires Monte Carlo modeling, not closed-form math.
FAQ
Can I model uneven cash flows here?
No — this calculator assumes constant PMT. For uneven cash flows, use the NPV or IRR calculators which discount each period separately.
Why does PMT for FV differ from PMT for amortization?
FV-target PMT solves for contributions that grow to a future amount. Amortizing PMT solves for the payment that reduces a present-value debt to zero. Same formula, different unknown.
What rate of return should I assume?
For long-horizon retirement planning, 6-7% nominal (4-5% real after inflation) is the conservative consensus. For short horizons, use current Treasury yields.
Are annuity calculators standardized?
The math is standard. Display conventions and rounding rules vary. For audit-grade work, use Excel's PMT, PV, FV functions or the HP-12C.
Does this handle Roth vs traditional tax effects?
Not directly. Compute pretax, then apply a marginal tax rate to model after-tax outcomes for each account type.
How accurate over multi-decade horizons?
Highly accurate as a math exercise — exact. The variance is in the assumed rate of return, which over 30+ years can produce outcomes 30-50% above or below the central projection.