Annuity Calculator
Solve for any annuity variable — payment, present value, future value, term, or interest rate — using standard time-value-of-money formulas.
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How to use this calculator
PMT = periodic payment, r = periodic interest rate, n = number of periods. Rearrange to solve for whichever variable is unknown.
- 1
Select what you want to solve for: payment, present value, future value, term, or rate.
- 2
Fill in the known values — the field corresponding to your chosen mode is the unknown.
- 3
The calculator displays the solved value along with a summary of total paid and interest.
- 4
Switch modes to explore different scenarios: e.g. find the rate your annuity earns, or the term needed.
Frequently asked questions
What formulas does this tool use?
With r = annual rate ÷ 100 ÷ 12 and n in months, this tool uses PV = PMT × [1 − (1 + r)^−n] ÷ r + FV ÷ (1 + r)^n for present value, and FV = PMT × [(1 + r)^n − 1] ÷ r + PV × (1 + r)^n for future value. Payment, term and rate are rearrangements of the first equation. At r = 0 the annuity factor is replaced by n.
Ordinary annuity or annuity due?
Ordinary: every payment falls at the end of its month. For payments at the start of each month, multiply a present or future value by (1 + r), or divide a payment by (1 + r). The tool has no switch, so apply that adjustment yourself.
Are periods and the rate monthly?
Yes. Periods are entered in months and the annual rate is divided by 12, so 6% is 0.5% a month. When solving for rate, the monthly result is multiplied by 12, giving a nominal annual rate and not an effective one: 0.31% a month shows as 3.74%.
What is the Future Value field in the other modes?
A lump sum paid at the end of the term, discounted by (1 + r)^n, as with a balloon payment on a loan. In payment mode, 20,000 now with 5,000 due after 60 months at 4% needs 292.91 a month. The tool does not treat it as a savings target, so it cannot work out how long a savings goal takes.
Why does Number of Periods say no valid solution?
If the payment does not exceed the interest accruing each month, the balance never falls. With 100,000 at 6% the interest is 500 a month, so a 400 payment gives an error. The result is also an error when the inputs imply a negative or infinite number of months.
How is a non-whole number of periods handled?
It is rounded up to a whole month. The tool then adds a smaller final payment so that the balance clears exactly: 100,000 at 6% with 1,000 a month takes 139 months, with a final payment of 975.78 and a total paid of 138,975.78. That total excludes any FV you entered.
What does it exclude?
Growing or declining payments, payment timing at the start of the period, taxes, fees and inflation. A 0% rate is respected and just adds payments. The output is an illustration from your inputs and not a forecast or advice.
Annuity maths: solving for payment, value, term or rate
One equation, five unknowns
An annuity here is a run of equal monthly payments. Present value is those payments discounted to today, and future value is the same payments compounded forward. The calculator keeps one equation and solves it for whichever quantity you choose: payment, present value, future value, number of months or interest rate. The first two and the fourth have closed-form answers, while the rate has to be searched for.
Worked examples in three modes
Solving for payment on 100,000 at 6% over 120 months gives $1,110.21, so total paid is $133,224.60 and interest $33,224.60. Solving for present value, 500 a month at 5% for 240 months is worth $75,762.66 against $120,000.00 of total payments. Solving for future value, 500 a month at 6% for 240 months builds to $231,020.45, of which $111,020.45 is growth.
Solving for term and rate
The table collects runs from each mode. Term and rate are the harder two: term needs a payment larger than the monthly interest, and rate is found by searching between a monthly −50% and +500%. When payments add up exactly to the amount borrowed, the solved rate is 0.00% and the tool shows it as such.
| Mode and inputs | Result |
|---|---|
| Payment: PV 100,000, 6%, 120 months | $1,110.21 a month |
| Payment: PV 20,000, FV 5,000, 4%, 60 months | $292.91 a month |
| Present value: 500 a month, 5%, 240 months | $75,762.66 |
| Future value: 500 a month, 6%, 240 months | $231,020.45 |
| Term: PV 100,000, 1,000 a month, 6% | 139 months (11.6 years) |
| Rate: PV 100,000, 1,000 a month, 120 months | 3.74% a year (0.31% a month) |
| Rate: PV 12,000, 1,000 a month, 12 months | 0.00% a year |
Why a loan is an annuity
A fixed-payment loan is the same equation seen from the lender’s side: the amount borrowed is the present value and the instalment is the payment. That is why the payment mode reproduces a standard instalment and why the term mode fails when the instalment cannot cover the interest. A balloon payment at the end is handled by the Future Value field.
Inputs and their limits
The tool assumes level payments at month-end, a constant rate and no charges. Payments that grow or fall, start-of-month timing and taxes are outside it. Whichever mode you pick, the answer is an illustration of the arithmetic from your inputs, so compare scenarios with it and do not read the output as a forecast. Switching modes keeps the other fields where you left them, so a Future Value you set for one calculation still counts in the next; clear it to 0 when you want a plain level-payment stream.
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