Annuity Calculator

An annuity calculator works with a series of equal payments. The future value of regular deposits is FV = PMT × ((1 + i)^N − 1) ÷ i, where i is the rate per period and N is the number of payments. For example, $500 deposited at the end of every month for 20 years at 5% a year (i = 0.05 ÷ 12) grows to $205,516.83.

How to use the annuity calculator

1. Pick a tab. Future value grows regular deposits. Present value finds the lump sum that pays a set income. Payout turns a lump sum into a payment. How long it lasts counts the payouts a balance covers.
2. Enter the amounts, the yearly interest rate and the number of years.
3. Choose how often payments happen and how often interest compounds. If you are not sure, leave compounding at Per payment.
4. Choose the timing: end of each period (ordinary annuity) or start of each period (annuity due).
5. To make payments rise each year, for example with a cost-of-living raise, enter a yearly increase. That makes it a growing annuity.
6. Read the answer, then open Show steps for the working and the year-by-year schedule for every year.

Annuity formulas

All four tabs use the same building blocks. Let PMT be the payment, r the yearly rate, m the payments per year, i = r ÷ m the rate per period and N = years × m the number of payments.

• Future value (ordinary annuity): FV = PMT × ((1 + i)^N − 1) ÷ i
• Present value (ordinary annuity): PV = PMT × (1 − (1 + i)^−N) ÷ i
• Payment from a lump sum: PMT = PV × i ÷ (1 − (1 + i)^−N)
• Number of payments: N = −ln(1 − PV × i ÷ PMT) ÷ ln(1 + i)
• Annuity due: multiply the FV or PV factor by (1 + i), because every payment is one period earlier.

If a starting balance S is already invested, it grows separately as S × (1 + i)^N, and you add that to the future value of the deposits. When interest compounds at a different frequency c than the payments, the calculator first converts the rate: i = (1 + r ÷ c)^{c ÷ m} − 1.

Future value of an annuity: worked example

You have $10,000 and add $500 at the end of each month for 20 years at 5% a year.

1. Rate per month: i = 0.05 ÷ 12 ≈ 0.00416667. Number of deposits: N = 20 × 12 = 240.
2. Growth factor: (1.00416667)²⁴⁰ ≈ 2.712640.
3. The $10,000 grows to 10,000 × 2.712640 = $27,126.40.
4. The deposits grow to 500 × (2.712640 − 1) ÷ 0.00416667 = 500 × 411.033669 ≈ $205,516.83.
5. Total: $27,126.40 + $205,516.83 = $232,643.24 (to the cent, using the unrounded factors). You paid in $130,000, so interest earned $102,643.24.

Ordinary annuity vs annuity due

In an ordinary annuity each payment comes at the end of the period. Loan payments and most savings plans work this way. In an annuity due each payment comes at the start, like rent. Every payment then earns one extra period of interest, so the result is (1 + i) times larger. The $500 monthly deposits above grow to $205,516.83 as an ordinary annuity and to $206,373.15 as an annuity due. For payouts, the annuity due needs a slightly larger lump sum, because the first payment goes out at once.

Present value and payout examples

Lump sum for an income. To receive $2,000 at the end of each month for 25 years at 5%, N = 300 and the factor is (1 − 1.00416667⁻³⁰⁰) ÷ 0.00416667 ≈ 171.060047. You need 2,000 × 171.060047 ≈ $342,120.09 today. The payouts add up to $600,000. Interest on the money not yet paid out covers the difference.

Payout from a lump sum. Turned around, $300,000 at 5% for 25 years pays 300,000 ÷ 171.060047 ≈ $1,753.77 a month.

How long money lasts. $300,000 at 5% paying $2,000 a month gives N = −ln(1 − 300,000 × 0.00416667 ÷ 2,000) ÷ ln(1.00416667) ≈ 235.89. That is 235 full payments and a smaller final one, so the money lasts 19 years 8 months. If the monthly interest is at least as large as the payout, the balance never shrinks.

Growing annuity formula

When payments rise by g each year, value one year of payments first, a = (1 − (1 + i)^−m) ÷ i, then add the years as a geometric series with ratio q = (1 + g) ÷ (1 + i)^m:

PV = PMT × a × (1 − q^Y) ÷ (1 − q)

For $2,000 a month rising 2% a year for 25 years at 5%: a ≈ 11.681222, q ≈ 0.970355 and (1 − q²⁵) ÷ (1 − q) ≈ 17.835480, so PV ≈ $416,680.40. That is about $74,560 more than the level $2,000 income needs, which shows what a cost-of-living raise costs.

Monthly payout per $100,000 (quick reference)

Level payments at the end of each month that use up $100,000 exactly, with the interest rate compounded monthly. These are math results, not insurance quotes.

Annuity math vs annuity products

In math, an annuity is any stream of regular payments: a savings plan, a loan or a pension. An annuity you buy is an insurance contract, and a few general facts about these contracts come from the regulators’ investor pages:

• Investor.gov (SEC) says fixed annuities guarantee at least a minimum interest rate during the accumulation phase. Fixed annuities are insurance products regulated by state insurance regulators, not the SEC.
• Payments depend on the insurer’s finances. Investor.gov warns that an insurer in financial difficulty may not be able to pay.
• Surrender charges can apply if you withdraw money within a set number of years. Investor.gov notes that fees reduce the value of an annuity however you pay them.
• FINRA explains that earnings grow tax-deferred and withdrawals are taxed as ordinary income. Withdrawals before age 59½ can face a 10% penalty.

A life annuity quote also depends on your age and life expectancy, so it will not match a fixed-term calculation. Use this calculator to understand the math and to check a contract’s stated figures. Ask the insurer for its exact numbers, and read the contract before you buy.

Common annuity calculation mistakes

• Using the yearly rate as the rate per period. With monthly payments, divide by 12 (or convert it if compounding differs).
• Mixing up timing. An annuity due multiplies the result by (1 + i).
• Counting years instead of payments in the exponent. 20 years of monthly payments means N = 240.
• Comparing a fixed-term payout with a life annuity quote. They answer different questions.
• Forgetting fees, surrender charges and taxes, which this calculator leaves out.

Results are estimates for learning and planning, not financial advice.

Sources

Product facts were checked November 2026:

• Investor.gov (SEC): Annuities
• FINRA: Annuities

Annuity practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is the formula for an annuity?

For payments at the end of each period, the future value is PMT × ((1 + i)^N − 1) ÷ i and the present value is PMT × (1 − (1 + i)^−N) ÷ i. Here i is the rate per period and N is the number of payments. For an annuity due, multiply either one by (1 + i).

How much does a $100,000 annuity pay per month?

Spread over a fixed term, the math gives $659.96 a month for 20 years at 5%, or $536.82 for 30 years. An insurer's life annuity quote is different. It depends on your age, life expectancy, the payout options and the insurer's rates, so ask the insurer for a quote.

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

The timing. Ordinary annuity payments come at the end of each period, and annuity due payments at the start. An annuity due is worth (1 + i) times as much, because each payment has one more period to earn interest.

How long will $300,000 last with $2,000 a month?

At a steady 5% a year compounded monthly, about 19 years 8 months: 235 full payments and a smaller final one. With no interest it would last exactly 150 months (12 years 6 months).

What is a growing annuity?

A growing annuity is a stream of payments that rises at a steady rate, for example 2% a year to keep up with prices. Its present value uses a geometric series. Enter the yearly increase in the calculator to see the effect.

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