An annuity is a series of equal payments at regular intervals for a set number of periods. Savings deposits, loan payments, rent, and many insurance style payouts follow this pattern. This calculator values level payment streams using standard time value of money formulas.

Annuity Calculator

Future value · Present value · Payment · Ordinary or due

Timing

Payment type ?

Frequency

Rate and term

Annual rate % ?

Years

Starting principal ?

Payment per period

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Level payment annuity math. Not a life insurance quote, tax projection, or mortality based payout product.

📆 Enter rate, years, and payment details to see PV, FV, or required payment.

Future value

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Total payments

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Interest earned

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Periods

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ANNUITY

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Period rate

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Periods (n)

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Payment (PMT)

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Present value

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Future value

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Timing

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Ordinary annuity result

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Payments at period end

Annuity due result

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Payments at period start (= ordinary × (1+r))

Calculation used

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Balance over periods

Period schedule

First 24 periods

#	Payment	Interest	Balance

Annuity Formulas

Let r be the interest rate per payment period and n the number of payments. PMT is the level payment each period.

Future value (ordinary)

FV = PMT × ((1 + r)^n − 1) ÷ r If starting principal S exists: add S × (1 + r)^n Example: S = $20,000, PMT = $10,000, r = 6%, n = 10, due → FV = $175,533.38

Present value (ordinary)

PV = PMT × (1 − (1 + r)^(−n)) ÷ r Example: $500 / month for 20 years at 5% annual → PV ≈ $75,762.66

Annuity due

PV_due = PV_ordinary × (1 + r) FV_due = FV_ordinary × (1 + r)

What This Calculator Solves

Future value: end balance from starting principal plus regular deposits
Present value: lump sum today equal to a future payment stream
Payment → goal: deposit needed to reach a target FV
Payout: level withdrawal from a starting lump sum over the term

Choose ordinary or due timing and annual, semi annual, quarterly, or monthly frequency. Results show both ordinary and due values so you can compare timing quickly.

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Rent and many lease or insurance premiums are annuity due. Most loan payments and bond coupons are ordinary annuities.

What Is an Annuity?

In finance, an annuity is a stream of equal cash flows at regular intervals for a fixed number of periods. The word is also used for insurance products that convert a premium into income. This page focuses on the cash flow math: present value, future value, and payment size for level streams.

FINRA explains that insurance annuities come in several product types with fees, riders, and surrender terms. Treat product quotes separately from the textbook formulas used here.

Ordinary annuity versus annuity due

Ordinary annuities pay at the end of each period. Annuity due pays at the beginning. Due payments earn one extra period of interest, so both PV and FV are larger by the factor (1 + r).

How to use this calculator

Pick Future value, Present value, Payment → goal, or Payout.
Set ordinary or due timing and payment frequency.
Enter annual rate and years. The tool sets r = annual rate ÷ frequency and n = years × frequency.
Enter payment, starting principal, target FV, or payout lump sum as required by the mode.
Read the hero result, ordinary versus due comparison, formula strip, chart, and schedule.

Worked example: accumulation (matches common annual due case)

Starting principal $20,000. Annual payment $10,000 for 10 years. Annual rate 6%. Annuity due.

r = 0.06, n = 10. Grown principal = 20,000 × 1.06^10 = $35,816.95. Ordinary FV of payments = 10,000 × ((1.06^10 − 1) ÷ 0.06) = $131,807.95. Due FV of payments = 131,807.95 × 1.06 = $139,716.43. Total FV = 35,816.95 + 139,716.43 = $175,533.38.

Worked example: monthly ordinary savings

Deposit $500 at the end of each month for 20 years at 5% nominal annual. r = 0.05 ÷ 12, n = 240. FV ≈ $205,516.83. PV of the same stream ≈ $75,762.66.

Payment to reach a goal

Ordinary PMT from FV = FV × r ÷ ((1 + r)^n − 1). If there is a starting principal, subtract its future value from the target first: PMT uses (target − S(1+r)^n). For due timing, divide the ordinary payment by (1 + r).

Payout from a lump sum

Ordinary PMT from PV = PV × r ÷ (1 − (1 + r)^(−n)). This is the level amount you can withdraw each period so the balance reaches about zero after n periods at rate r, assuming no extra fees or taxes.

Common mistakes

Mixing annual rate with monthly periods without dividing the rate
Using ordinary timing for rent style beginning payments
Forgetting starting principal when projecting accumulation
Treating a guaranteed insurance product rate as identical to an assumed investment return
Ignoring taxes, fees, and mortality when comparing insurance annuity quotes

When this calculator is useful

Use it for savings plans, comparing payment timing, sizing deposits toward a goal, estimating a fixed term withdrawal plan, or checking homework style annuity problems.

When it may not be enough

It does not price variable annuities, living benefits, surrender charges, or life contingent payouts. It does not replace advice from a licensed professional. For full TVM with odd cash flows, use the Finance Calculator. For PV only problems, see the Present Value Calculator.

Related tools

Compound Interest, Investment, Savings, Retirement, and Loan calculators cover nearby planning questions.

Calculation Methodology

Set frequency m (1, 2, 4, or 12). Period rate r = (annual % ÷ 100) ÷ m. Periods n = years × m.
Compute ordinary PV and FV factors. Multiply by (1 + r) when timing is annuity due.
Future value mode: FV = S(1+r)^n + PMT × FV factor.
Present value mode: PV = PMT × PV factor (starting principal field is not used).
Payment → goal: solve PMT from the FV equation after growing any starting principal.
Payout: solve PMT from the PV equation using the lump sum as PV.
Build a period schedule by applying interest and payments in order for the selected timing.

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Results are educational estimates. They are not financial, tax, or insurance advice.

Reference Examples

Scenario	Result
$20k start + $10k / yr due, 6%, 10 yr	FV $175,533.38
$500 / mo ordinary, 5%, 20 yr	FV ≈ $205,517
Same monthly stream	PV ≈ $75,763
$100k payout, 4%, monthly, 20 yr ordinary	PMT ≈ $605.98

Enter your own numbers above for exact schedule interest and ending balances.

Frequently Asked Questions

What is an annuity?

An annuity is a series of equal payments at regular intervals for a set term. This calculator values those cash flows. Insurance annuity products add fees and contract terms beyond the basic formulas.

What is the difference between an ordinary annuity and an annuity due?

Ordinary pays at period end. Due pays at period start. Due PV and FV equal the ordinary results times (1 + r).

What is the future value of an annuity formula?

Ordinary FV = PMT × ((1 + r)^n − 1) ÷ r. Multiply by (1 + r) for due. Add starting principal grown by (1 + r)^n when relevant.

What is the present value of an annuity formula?

Ordinary PV = PMT × (1 − (1 + r)^(−n)) ÷ r. Multiply by (1 + r) for annuity due.

How do I find the payment needed to reach a savings goal?

Use Payment → goal. Enter target FV, rate, years, frequency, and timing. The calculator solves for the level deposit each period.

Is this the same as an insurance annuity quote?

No. Product quotes may include mortality, fees, riders, and guarantees. Use this tool for level cash flow math and compare contract details with a licensed advisor when buying a product.

Sources & References

FINRA — Annuities investor information: finra.org/investors/investing/investment-products/annuities
Investor.gov (SEC Office of Investor Education) — Annuities overview: investor.gov annuity basics

Methodology reviewed: 2026. Educational use only.