Annuity Calculator
Solve the present value, future value or payment of a level annuity — ordinary or due — from rate and periods, with the time-value-of-money formulas shown.
Annuity Calculator: with the default inputs, result is $94,281.35.
Used when solving for present or future value.
Used when solving for the payout a lump sum funds.
Used when solving for the payment needed to reach a target.
- In words
- $1,000.00 at the end of each month for 120 months at 5% is worth $94,281.35 today.
- Sum of all payments
- $120,000.00
- Interest component
- $25,718.65Difference between the payments and the lump sum — what the time value of money contributes.
- Annuity factor
- 94.28135Value of a 1-per-period annuity; multiply by any payment to scale.
Assumptions
- Level payments, a constant rate compounded once per payment period, and no fees, taxes or mortality adjustments.
How this is worked out
The formula
i = annual rate ÷ payments per year, n = number of payments Ordinary annuity (payments at end of period): PV = PMT × [ 1 − (1 + i)^−n ] ÷ i FV = PMT × [ (1 + i)^n − 1 ] ÷ i PMT = PV × i ÷ [ 1 − (1 + i)^−n ] or PMT = FV × i ÷ [ (1 + i)^n − 1 ] Annuity due (payments at start of period): multiply PV or FV by (1 + i); divide PMT by (1 + i)
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Solve for
- Choose one of 4 options.Present value of a series of payments · Future value of a series of payments · Payment a lump sum can fund (payout) · Payment needed to reach a future value
- Payment per period
- Used when solving for present or future value.in dollars · 0 or more · defaults to 1000
- Present value (lump sum today)
- Used when solving for the payout a lump sum funds.in dollars · 0 or more · defaults to 100000
- Future value (target)
- Used when solving for the payment needed to reach a target.in dollars · 0 or more · defaults to 100000
- Annual interest rate
- A number.a percentage · from 0 to 100 · defaults to 5
- Payments per year
- Choose one of 4 options.Monthly · Quarterly · Semiannually · Annually
- Number of payments
- A number.from 1 to 1200 · whole numbers only · defaults to 120
- Payment timing
- Choose one of 2 options.End of period (ordinary annuity) · Start of period (annuity due)
What you get back
- Resultmain answer
- In words
- Sum of all payments
- Interest component
- Difference between the payments and the lump sum — what the time value of money contributes.
- Annuity factor
- Value of a 1-per-period annuity; multiply by any payment to scale.
What this assumes
- Level payments, a constant rate compounded once per payment period, and no fees, taxes or mortality adjustments.
About this calculator
An annuity, in the finance-textbook sense, is any series of equal payments at regular intervals: a mortgage, a car loan, a pension payout, monthly savings deposits, a lottery paid over 20 years. The same four formulas value all of them. This calculator solves whichever quantity you're missing and shows the factor it used, so you can check a bank's numbers or a homework problem.
The four questions
- Present value: what is a stream of payments worth as a lump sum today? (Is the $1,000-a-month pension worth more than the $150,000 buyout?)
- Future value: what will regular deposits grow to? ($500 a month for 10 years at 5%?)
- Payment from a lump sum: how much can a pot pay out each period until it's gone? (Also the loan payment on a mortgage — a loan is just a lump sum you received.)
- Payment to reach a target: how much to save each period to hit a future amount?
Ordinary vs due
An ordinary annuity pays at the end of each period — loans and most bonds. An annuity due pays at the start — rent, leases, insurance premiums, and pension payments made in advance. Every payment in an annuity due arrives one period earlier, so its value is exactly (1 + i) times the ordinary version. Pick the timing that matches your contract; on a 10-year monthly stream at 5% the difference is about 0.4%.
Reading the results
The result is the solved quantity. Sum of all payments is the plain cash total, and the interest component is the gap between that and the lump sum — the price or reward of time. The annuity factor is the value of a 1-per-period stream; multiply it by any payment to scale up without recomputing.
Insurance annuities
The products sold by insurers — fixed, indexed, variable, immediate, deferred — are contracts that promise an income, often for life rather than a fixed number of payments. Their pricing uses these formulas plus mortality tables, fees and guarantees you can't see from outside. This calculator values the payment stream you're quoted at a rate you choose, which is the right first step in judging whether such a product is fairly priced: if the implied rate is well below what a Treasury ladder pays, the guarantee is expensive.
Frequently asked questions
▸What is the present value of an annuity?
The lump sum today that's equivalent to a series of future payments at a given rate: PV = PMT × [1 − (1 + i)^−n] ÷ i. $1,000 a month for 10 years at 5% is worth $94,281 today, not $120,000, because later payments are discounted.
▸What's the difference between an ordinary annuity and an annuity due?
Timing. Ordinary annuities pay at the end of each period (loans); annuities due pay at the start (rent). An annuity due is worth (1 + i) times the ordinary one because each payment arrives one period sooner.
▸Is a loan payment an annuity calculation?
Yes. The lender gives you a present value (the loan) and you repay an ordinary annuity; the payment formula here with the loan amount as PV gives exactly the standard mortgage payment.
▸How do I value a pension buyout offer?
Solve for the present value of the monthly pension over your expected remaining life at a rate you could safely earn (e.g. a Treasury yield). If the offered lump sum is smaller than that PV, the pension is the better deal, before considering inflation protection and longevity risk.
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