An annuity is a stream of equal payments made at regular intervals, and it shows up almost everywhere in personal finance: a monthly pension payout, a car loan, a lease, a structured settlement, or a dedicated savings plan where you put the same amount aside every payday. The two questions people actually want answered are: what is that future stream of payments worth in today's dollars (its present value, or PV), and what will it grow into by the end (its future value, or FV)? This annuity calculator computes both instantly from the payment amount, the interest rate, the time horizon, and how often you pay.
Adjust the sliders and every figure updates on the spot. Switch between an ordinary annuity (payments at the end of each period) and an annuity due (payments at the start) to see how the timing of a single payment shifts the result.
How to Use
- Enter the Regular Payment (PMT) — the fixed amount you pay into or receive from the annuity each period. For a monthly pension this is your monthly check; for a savings plan it is the automatic transfer.
- Set the Interest Rate (APR). This is the annual rate used to discount future payments back to today (for PV) or to grow them forward (for FV). If you are comparing a guaranteed annuity to an investment account, plug in the expected long-term return on that account.
- Choose the Number of Years over which the payments run. A 30-year mortgage is an annuity; a 10-year savings plan is an annuity; a 20-year pension payout is an annuity.
- Pick the Payment Frequency — monthly (12), quarterly (4), or annual (1). The calculator converts the annual rate into a periodic rate and the years into a total number of periods automatically.
- Select the Annuity Type. Ordinary means payments arrive at the end of each period (most loans, bonds, and mortgages). Due means payments arrive at the start (rent leases, annuity contracts that begin immediately).
- Read the result card. The highlighted Present Value tells you what the whole stream is worth today; the Future Value tells you what it compounds to; Total Contributions is simply PMT times the number of periods, and Total Interest is the gap between FV and contributions.
The Annuity Formulas
For an ordinary annuity (end-of-period payments), the present and future values come from the two standard formulas used in every finance textbook, the CFA curriculum, and spreadsheets:
PV = PMT × (1 − (1 + r)⁻ⁿ) / r
FV = PMT × ((1 + r)ⁿ − 1) / r
Where:
- PMT is the regular payment each period.
- r is the periodic interest rate — the annual APR divided by the number of payments per year.
- n is the total number of periods — years times payments per year.
Worked example: pay $1,000 at the end of every month for 10 years at a 5.0% annual rate. The periodic rate is 0.05 / 12 = 0.004167 and n = 120. The present value is about $94,281 and the future value is about $155,282. You contributed $120,000 in total, so the account earned roughly $35,282 in interest by the end.
If the rate is 0%, both formulas divide by zero, so the engine simply multiplies the payment by the number of periods: $500 a month for 5 years is exactly $30,000 today and $30,000 in the future, with no interest at all.
For an annuity due, each payment lands one period earlier, so every cash flow earns one extra period of interest. The engine multiplies both PV and FV by (1 + r). On the same $1,000 monthly, 10-year, 5% stream, switching to annuity due lifts the present value to about $94,674 and the future value to about $155,929 — a modest but real boost from pulling the payments forward.
Ordinary Annuity vs Annuity Due
The timing of a payment matters because of the time value of money. A dollar today can be invested; a dollar next year cannot.
- Ordinary annuity (end of period): mortgage payments, auto loans, bond coupon payments, most structured settlements. Payments are made after the period of use.
- Annuity due (start of period): rent, lease payments, annuity contracts that begin immediately, insurance premiums. Payments are made in advance.
Because annuity due payments arrive one period sooner, its present and future values are always higher than the otherwise-identical ordinary annuity. The difference is exactly one period of compounding: multiply the ordinary result by (1 + r).
Why Present and Future Value Matter
These two numbers answer very different real-world questions:
- Present value helps you decide whether a quoted annuity price is fair. If a lottery offers you a $500,000 lump sum today or $50,000 a year for 20 years, the present value of the payment stream (discounted at your expected return) tells you which offer is worth more. If PV is $620,000, the installments are the better deal; if PV is $440,000, take the cash.
- Future value helps you plan a savings goal. If you can put aside $1,000 a month and expect a 6% return, FV tells you what that monthly discipline will be worth in 20 or 30 years — and it is usually far larger than people expect, because of compound growth.
Examples
Example 1 — A 10-year monthly savings plan. You invest $1,000 at the end of each month for 10 years at 5.0% APR. The periodic rate is 0.4167% and there are 120 periods. The calculator shows a present value of about $94,281 and a future value of about $155,282. Your out-of-pocket contributions are $120,000, so compounding added roughly $35,282.
Example 2 — A zero-rate comparison. You put away $500 at the end of each month for 5 years in an account that pays no interest. With r = 0, present value and future value both equal $30,000 — exactly your contributions, with no interest earned. This is the honest baseline: without a positive return, an annuity does not grow at all.
Example 3 — A large annual pension payout. A retiree receives $1,000,000 at the end of each year for 8 years, discounted at 4.0% APR. The present value of this stream is about $6.73 million and the future value at the end of year 8 is about $9.21 million. The retiree collects $8,000,000 in total; the difference between FV and contributions is the interest earned along the way.
FAQ
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity makes payments at the end of each period (mortgages, auto loans, bond coupons). An annuity due makes payments at the start of each period (rent, leases, immediate annuity contracts). The annuity due result is always higher because every payment earns one extra period of interest; mathematically you multiply the ordinary PV and FV by (1 + r).
How is the present value of an annuity calculated?
The present value uses the formula PV = PMT × (1 − (1 + r)⁻ⁿ) / r, where PMT is the periodic payment, r is the periodic interest rate (annual APR divided by payments per year), and n is the total number of periods (years times payments per year). This discounts every future payment back to today and sums them.
How is the future value of an annuity calculated?
The future value uses FV = PMT × ((1 + r)ⁿ − 1) / r. It projects each payment forward to the end of the final period at the periodic rate and sums the growing balances. For an annuity due, multiply the result by (1 + r).
What does a negative payment amount mean?
The calculator requires the regular payment to be a positive number. A negative PMT would flip the sign of both PV and FV and produce a meaningless result, so the engine rejects it instead of returning a nonsense value. Enter what you actually pay or receive each period as a positive amount.
Is this calculator suitable for retirement planning?
It is a planning aid, not a personalized recommendation. Use it to compare a lump-sum offer against installment payments, to project a regular savings plan, or to price a stream of future cash flows. Actual annuity contracts include fees, mortality credits, and insurer guarantees that this simple formula does not capture, so confirm numbers with a licensed fiduciary before committing.
What happens when the interest rate is zero?
The standard formulas divide by r, so at r = 0 they are undefined. The engine falls back to PMT × n for both PV and FV, which is correct: with no interest, 60 payments of $500 are worth exactly $30,000 today and exactly $30,000 at the end, with zero interest earned.
Disclaimer
This annuity calculator is provided for informational purposes only and does not constitute financial, investment, tax, or insurance advice. Estimates are based on the standard ordinary-annuity formulas and the inputs you enter; actual annuity contracts, guaranteed income riders, fees, and insurer solvary differ. Always verify figures with a qualified financial professional or licensed annuity specialist before making a purchase or distribution decision.