How to use the annuity calculator
- Choose what to find: the future value of regular payments, the present value of regular payments, or the payment a lump sum can fund.
- Enter the payment (or the lump sum), the annual interest rate and the term in years.
- Pick the payment frequency and whether payments are made at the end of each period (ordinary annuity) or at the start (annuity due).
- Read the headline result and the year-by-year table. Download the CSV or PDF to keep the schedule.
Formula
i = annual rate / payments per year; n = payments per year x years
Future value (ordinary) = PMT x ((1 + i)^n - 1) / i
Present value (ordinary) = PMT x (1 - (1 + i)^-n) / i
Payment from a lump sum L = L x i / (1 - (1 + i)^-n)
Annuity due: multiply future and present value by (1 + i), or divide the payment by (1 + i)
At a 0% rate every formula reduces to simple multiplication: future value = PMT x n and the payment from a lump sum is L / n.
Worked examples
Saving with an annuity: paying $500 a month for 20 years at 5% (240 payments, i = 0.4167% a month) grows to $205,516.83 with end-of-month payments. You pay in $120,000, so $85,516.83 is interest. Paying at the start of each month gives $206,373.15.
Present value: the same 240 payments of $500 are worth $75,762.66 today at a 5% discount rate, or $76,078.33 as an annuity due. Total payments are $120,000, so discounting removes the rest.
Payout from a lump sum: $250,000 at 5% paid out monthly over 20 years supports $1,649.89 a month (end of month) or $1,643.04 (start of month). With a 0% rate, $100,000 over 10 yearly payments is $10,000.00 each.
Ordinary annuity versus annuity due
An ordinary annuity pays at the end of each period, like a mortgage or a bond coupon. An annuity due pays at the start, like rent or an insurance premium. Because each due payment is one period earlier, it earns or costs one extra period of interest, so its value is higher by a factor of (1 + i). On the $500 monthly example the difference over 20 years is $856.32.
Using this for real annuity products
This tool does the mathematics of a fixed-rate stream of equal payments. A commercial annuity from an insurer also builds in fees, a guaranteed rate that may differ from the rate you assume, life expectancy and sometimes surrender charges. Treat the numbers here as a way to understand how rate and term drive a payment, not as a quote for any product.
The payout mode assumes the money earns the rate you enter until the last payment, which leaves a balance of zero. It does not model an income that lasts for life.
How to read the year-by-year table
For future value, the table shows the payments made in the year, the interest earned and the balance at year end. For present value and payouts, the table starts with the present value or lump sum and shows what is paid out, the interest credited and what remains. The final remaining balance is $0.00, which is a quick check that the payment is right.
Assumptions and limits
- Interest compounds at the same frequency as the payments, with the rate you enter divided by the payments per year.
- The term must be a whole number of payments. A 2.5-year term is allowed for monthly payments but not for annual ones.
- The rate is constant for the whole term, and payments are all equal.
- Taxes, fees, surrender charges, inflation, life expectancy and insurer guarantees are not modeled.
- The 5% rate in the example is an illustration, not current market data.
- Informational only. This is not advice or a quote for an annuity product.
Frequently asked questions
What is the difference between present value and future value of an annuity?
Future value is what a series of payments grows to by the end, with interest. Present value is what that series of payments is worth today, discounted at the rate. They describe the same payments at two different dates.
What is an annuity due?
An annuity due makes each payment at the start of the period instead of the end. Every payment then has one more period to earn interest, so its future value is higher than an ordinary annuity by a factor of one plus the periodic rate.
How is the payout from a lump sum calculated?
The payment is the level amount that, with interest at the rate you enter, uses up the lump sum exactly over the term. It is the same formula as a loan payment, with the lump sum playing the role of the loan amount.
Why does the term have to be a whole number of payments?
The formulas count complete payments. A term that leaves a partial period would need a smaller final payment, which this tool does not guess. Adjust the term or switch to a more frequent payment schedule.
Can I use this for a pension or an insurance annuity?
Only to understand the arithmetic. Real contracts add fees, life-contingent payments and their own rates. Ask the provider for an illustration, and use this tool to sanity check how much the rate and term matter.