An annuity is a series of equal payments made at regular intervals over time. Ordinary annuity: payments at end of each period (most loans, 401(k) contributions). Annuity due: payments at start of each period (leases, insurance premiums). Annuity due accumulates slightly more because each payment has one extra compounding period. Example: $500/month at 7%/year for 30 years (ordinary annuity) grows to $566,764. With annuity due timing, it grows to $570,121 — 0.6% more.

What is the future value of an annuity formula?

FV (ordinary annuity) = PMT × [(1 + r)^n − 1] / r, where PMT = payment per period, r = interest rate per period, n = number of periods. Example: $500/month, 7%/year (0.583%/month), 360 months → FV = $500 × [(1.00583)^360 − 1] / 0.00583 = $566,764. FV (annuity due) = FV × (1 + r). The [(1+r)^n − 1]/r factor is the future value annuity factor (FVAF). Doubling n does NOT double FV — compounding makes it grow much faster.

What is the present value of an annuity formula?

PV (ordinary annuity) = PMT × [1 − (1 + r)^−n] / r. This tells you the lump sum today that equals the value of all future payments. Example: $1,000/month for 15 years at 5%/year (0.417%/month) → PV = $1,000 × [1 − (1.00417)^−180] / 0.00417 = $127,834. This is how lenders price loans: the mortgage amount (PV) is the present value of all monthly payments. PV (annuity due) = PV × (1 + r). The [1−(1+r)^−n]/r factor is the present value annuity factor (PVAF).

How do I calculate the required payment for a target future value?

PMT = FV × r / [(1 + r)^n − 1] (ordinary annuity). Rearrange the FV formula to solve for payment. Example: target $100,000 in 10 years at 6%/year (0.5%/month, 120 periods) → PMT = $100,000 × 0.005 / [(1.005)^120 − 1] = $100,000 × 0.005 / 0.8194 = $610/month. For an annuity due, divide by (1 + r): $610 / 1.005 = $607/month. Use the "Solve for Payment" mode in this calculator to avoid manual formula entry.

What is the difference between an annuity and compound interest?

Compound interest: a single lump sum grows over time with no additional contributions. FV = PV × (1 + r)^n. Annuity: periodic equal contributions grow over time. The annuity formula adds the FV of each individual payment. Example: $10,000 lump sum at 7% for 30 years → $76,123 (compound interest). $500/month at 7% for 30 years → $566,764 (annuity). The annuity accumulates far more because of the ongoing contributions, not just the rate. Combining both: add a starting balance (PV) to the annuity formula to model a savings account with an existing balance plus regular contributions.

How do I use an annuity calculator for retirement planning?

For accumulation (how much will I have at retirement): use Future Value mode. Enter monthly contribution (PMT), years until retirement × 12 (n), expected annual return / 12 (r). Example: $600/month, 25 years, 7% return → $487,000 at retirement. For distribution (how much can I withdraw): use Present Value mode with your retirement nest egg as the target PV. For "how much do I need to save": use Payment mode with target FV. Key insight: starting early matters more than the amount — $300/month for 35 years at 7% ($497K) beats $600/month for 20 years ($328K) even though you contributed half as much total.

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Annuity Calculator

Ordinary annuity FV = PMT × [(1+r)^n − 1] / r. Example: $500/month at 7%/year (0.583%/month) for 360 months = $566,764. PV of annuity = PMT × [1 − (1+r)^−n] / r — used to price loans. Annuity due (start-of-period) multiplies by (1+r) for slightly higher FV. Required payment: PMT = FV × r / [(1+r)^n − 1]. The more time, the more compounding dominates total growth over contributions.

Calculate the future value, present value, or required payment for an ordinary annuity or annuity due. Solve for FV (retirement savings), PV (lump sum needed today), or payment (how much to save per period). Shows total contributions, interest earned, and a period-by-period growth schedule.

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Annuity Parameters

Solve For

Annuity Type

Payment per Period ($)

Interest Rate per Period (%)

Number of Periods

Present Value / Starting Balance ($)

Results

Future Value

$6,590.40

Present Value

$0.00

Total Contributions

$5,000.00

Interest Earned

$1,590.40

Growth Schedule

Period	Payment	Interest	Balance
1	$500.00	$0.00	$500.00
2	$500.00	$30.00	$1,030.00
3	$500.00	$61.80	$1,591.80
4	$500.00	$95.51	$2,187.31
5	$500.00	$131.24	$2,818.55
6	$500.00	$169.11	$3,487.66
7	$500.00	$209.26	$4,196.92
8	$500.00	$251.82	$4,948.73
9	$500.00	$296.92	$5,745.66
10	$500.00	$344.74	$6,590.40

Ordinary annuity: FV = PMT × [(1+r)^n − 1] / r. Payments at end of each period (most loans, retirement contributions). Annuity due: multiply by (1+r) — payments at start (leases, insurance premiums). PV = PMT × [1 − (1+r)^−n] / r for loan pricing.

How to Use

1
Choose what to solve for
Select "Future Value" to find what your savings will grow to. Select "Present Value" to find the lump sum equivalent today. Select "Payment" to find how much you need to save per period to hit a target.
2
Choose annuity type
Ordinary annuity (payments at end of period) covers most loans and investment contributions. Annuity due (payments at start) applies to leases and insurance premiums — it accumulates slightly more.
3
Enter the parameters
Fill in the payment amount (PMT), interest rate per period (r), and number of periods (n). For FV calculations, add a starting balance (PV = 0 if starting from scratch).
4
Read the result
The main result shows the solved value (FV, PV, or PMT). Below that: total contributions vs. interest earned — the difference shows how much of the growth comes from compounding.

Frequently Asked Questions

What is an annuity?: An annuity is a series of equal payments made at regular intervals over time. Ordinary annuity: payments at end of each period (most loans, 401(k) contributions). Annuity due: payments at start of each period (leases, insurance premiums). Annuity due accumulates slightly more because each payment has one extra compounding period. Example: $500/month at 7%/year for 30 years (ordinary annuity) grows to $566,764. With annuity due timing, it grows to $570,121 — 0.6% more.
What is the future value of an annuity formula?: FV (ordinary annuity) = PMT × [(1 + r)^n − 1] / r, where PMT = payment per period, r = interest rate per period, n = number of periods. Example: $500/month, 7%/year (0.583%/month), 360 months → FV = $500 × [(1.00583)^360 − 1] / 0.00583 = $566,764. FV (annuity due) = FV × (1 + r). The [(1+r)^n − 1]/r factor is the future value annuity factor (FVAF). Doubling n does NOT double FV — compounding makes it grow much faster.
What is the present value of an annuity formula?: PV (ordinary annuity) = PMT × [1 − (1 + r)^−n] / r. This tells you the lump sum today that equals the value of all future payments. Example: $1,000/month for 15 years at 5%/year (0.417%/month) → PV = $1,000 × [1 − (1.00417)^−180] / 0.00417 = $127,834. This is how lenders price loans: the mortgage amount (PV) is the present value of all monthly payments. PV (annuity due) = PV × (1 + r). The [1−(1+r)^−n]/r factor is the present value annuity factor (PVAF).
How do I calculate the required payment for a target future value?: PMT = FV × r / [(1 + r)^n − 1] (ordinary annuity). Rearrange the FV formula to solve for payment. Example: target $100,000 in 10 years at 6%/year (0.5%/month, 120 periods) → PMT = $100,000 × 0.005 / [(1.005)^120 − 1] = $100,000 × 0.005 / 0.8194 = $610/month. For an annuity due, divide by (1 + r): $610 / 1.005 = $607/month. Use the "Solve for Payment" mode in this calculator to avoid manual formula entry.
What is the difference between an annuity and compound interest?: Compound interest: a single lump sum grows over time with no additional contributions. FV = PV × (1 + r)^n. Annuity: periodic equal contributions grow over time. The annuity formula adds the FV of each individual payment. Example: $10,000 lump sum at 7% for 30 years → $76,123 (compound interest). $500/month at 7% for 30 years → $566,764 (annuity). The annuity accumulates far more because of the ongoing contributions, not just the rate. Combining both: add a starting balance (PV) to the annuity formula to model a savings account with an existing balance plus regular contributions.
How do I use an annuity calculator for retirement planning?: For accumulation (how much will I have at retirement): use Future Value mode. Enter monthly contribution (PMT), years until retirement × 12 (n), expected annual return / 12 (r). Example: $600/month, 25 years, 7% return → $487,000 at retirement. For distribution (how much can I withdraw): use Present Value mode with your retirement nest egg as the target PV. For "how much do I need to save": use Payment mode with target FV. Key insight: starting early matters more than the amount — $300/month for 35 years at 7% ($497K) beats $600/month for 20 years ($328K) even though you contributed half as much total.