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

Payment timing. An ordinary annuity pays at the END of each period — standard for bonds, mortgages, and most fixed annuities. An annuity due pays at the BEGINNING of each period — standard for rents, leases, and insurance. Because annuity-due payments are one period earlier, their PV and FV are multiplied by (1+r) relative to an otherwise identical ordinary annuity.

What is the present value of an annuity formula?

PV (ordinary) = PMT × (1 − (1+r)^-n) / r. For an annuity due, multiply the result by (1+r). Here PMT is the periodic payment, r is the periodic rate (as a decimal), and n is the total number of periods. Example: $500/month for 20 years at 6% APR (r = 0.06/12, n = 240) has PV = $69,790.39.

How do I calculate the future value of an annuity?

FV (ordinary) = PMT × ((1+r)^n − 1) / r. For an annuity due, multiply by (1+r). This tells you how much a series of equal payments will grow to by the end of the last period. Example: $200/month for 30 years at 7% annual (r = 0.07/12, n = 360) has FV = $243,994.

How do I find the annuity payment?

Rearrange the PV or FV formula for PMT. PMT from PV: PMT = PV × r / (1 − (1+r)^-n). PMT from FV: PMT = FV × r / ((1+r)^n − 1). For an annuity due, divide the result by (1+r). Our calculator does this automatically — pick 'Solve for Payment' mode.

What is an immediate annuity?

An immediate annuity is a contract where you hand an insurance company a lump sum and they begin paying you a fixed periodic income right away (typically within 1-12 months), for life or for a set number of years. The PV of the income stream should roughly equal the premium you paid, adjusted for the insurer's margin and mortality credits.

Does this calculator handle monthly annuities?

Yes. Enter the periodic rate and period count in the same cadence as the payment. For a monthly annuity with a 6% annual rate, use r = 0.5% per period (6 / 12) and n = 12 × years. For quarterly, use 1.5% per period (6 / 4) and n = 4 × years.

Annuity Calculator

An annuity is a series of equal payments made at regular intervals. Our annuity calculator handles the three core questions: (1) Present Value — how much a stream of future payments is worth today; (2) Future Value — how much a stream of payments will grow to by the end; and (3) Payment — the fixed payment that corresponds to a given PV or FV target. You can model ordinary annuities (payments at the end of each period, the default for most bonds, mortgages, and fixed annuity contracts) or annuities due (payments at the beginning of each period, the default for rents, leases, and insurance premiums). The difference is a multiplier of (1+r) — annuity due values are always slightly larger because each payment earns or discounts one additional period of interest.

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calendar_today Updated: April 2026

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savings Annuity Inputs

Solve For

Annuity Type

Periodic Payment

Rate per Period

Periods

Formula in use

PV = PMT × (1 − (1+r)^-n) / r

analytics Annuity Value

Present Value

$7,721.73

Ordinary annuity, 10 periods at 5%

Payment (PMT) $1,000.00

Present Value (PV) $7,721.73

Future Value (FV) $12,577.89

Total Paid In (nominal) $10,000.00

Implied Interest $2,577.89

Interpretation

Present value of $1,000 paid at the end of each period for 10 periods at 5% per period

Input Values

Solve For

Present Value (PV)

Future Value (FV)

Payment (PMT)

Annuity Type

Ordinary (end of period)

Annuity Due (beginning of period)

Periodic Payment ($)

Target PV / FV ($)

Periodic Interest Rate (%)

Number of Periods

tips_and_updates Tips

• Use an ordinary annuity (end of period) for bonds, mortgages, and fixed retirement payouts — it's the market default
• Use an annuity due (beginning of period) for rents, leases, and insurance premiums — anything paid upfront
• Annuity due PV and FV are always (1+r) bigger than an equivalent ordinary annuity because payments earn one extra period
• Match the period of r to the payment frequency: monthly payments need a monthly rate (annual ÷ 12), quarterly payments need annual ÷ 4
• Higher interest rate lowers PV (future payments are worth less today) but raises FV (payments grow faster)
• To size a retirement annuity, solve for PMT with PV = account balance, r = expected return, n = years × payment frequency
• Annuity PV is exactly the principal of a fully-amortizing loan with those payments — the two formulas are mirror images

How to Use This Calculator

Pick solve-for mode

Choose PV (discount payments to today), FV (compound payments to the end), or PMT (find the payment for a given PV or FV).

Pick annuity type

Ordinary (end of period) for bonds/mortgages/fixed annuities, or Annuity Due (beginning of period) for rents/leases/premiums.

Enter payment, rate, periods

Type the per-period payment, the per-period interest rate (as a percent), and the total number of periods. Make sure rate and period count match the payment frequency.

Read every value

The calculator returns PV, FV, and PMT together, plus total nominal payments and implied interest.

The Formula

For an ordinary annuity, payments occur at the end of each period. PV discounts each future payment back to today; FV compounds each payment forward to period n. An annuity due shifts every payment one period earlier, so multiply either result by (1+r). To solve for PMT, rearrange: PMT = PV × r / (1 − (1+r)^-n) or PMT = FV × r / ((1+r)^n − 1), then divide by (1+r) if the annuity is due.

PV (ordinary) = PMT × (1 − (1+r)^-n) / r | FV (ordinary) = PMT × ((1+r)^n − 1) / r | Annuity Due: × (1+r)

lightbulb Variables Explained

PMT Periodic payment amount
r Periodic interest rate (annual rate ÷ compounding per year, expressed as a decimal)
n Total number of periods
PV Present value — lump sum today equivalent to the payment stream
FV Future value — lump sum at the end equivalent to the payment stream

tips_and_updates Pro Tips

Use an ordinary annuity (end of period) for bonds, mortgages, and fixed retirement payouts — it's the market default

Use an annuity due (beginning of period) for rents, leases, and insurance premiums — anything paid upfront

Annuity due PV and FV are always (1+r) bigger than an equivalent ordinary annuity because payments earn one extra period

Match the period of r to the payment frequency: monthly payments need a monthly rate (annual ÷ 12), quarterly payments need annual ÷ 4

Higher interest rate lowers PV (future payments are worth less today) but raises FV (payments grow faster)

To size a retirement annuity, solve for PMT with PV = account balance, r = expected return, n = years × payment frequency

Annuity PV is exactly the principal of a fully-amortizing loan with those payments — the two formulas are mirror images

An annuity is simply a stream of equal payments at equal intervals. The two building-block formulas are: PV = PMT × (1 − (1+r)^-n) / r and FV = PMT × ((1+r)^n − 1) / r. Both assume payments at the end of each period (ordinary annuity). If payments happen at the beginning (annuity due), each payment gets one extra period of compounding or discounting, so multiply both PV and FV by (1+r). To solve for PMT, algebraically invert: PMT = PV × r / (1 − (1+r)^-n) for a given PV, or PMT = FV × r / ((1+r)^n − 1) for a given FV. This calculator always applies the (1+r) factor automatically when you pick 'annuity due'.

Use PRESENT VALUE when you know the payment stream and want today's lump-sum equivalent — pricing a bond coupon strip, valuing a pension, or figuring out how much principal backs a mortgage payment. Use FUTURE VALUE when you want to know what a regular contribution grows to — a sinking fund, a savings plan, or an annuity's accumulated balance at retirement. Use PAYMENT when you have a target (mortgage principal, retirement nest egg, bond face value) and want the equal payment that hits it — this is the same math as a loan amortization schedule.

Frequently Asked Questions

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tips_and_updates Tips

How to Use This Calculator

Pick solve-for mode

Pick annuity type

Enter payment, rate, periods

Read every value

The Formula

lightbulb Variables Explained

tips_and_updates Pro Tips

Frequently Asked Questions

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