Annuity Calculator
This annuity calculator finds the level payment a sum of money can fund, or the present value or future value of a series of payments. Example: 100,000 at 5% pays 659.96 a month for 20 years.
Example: What do you want to calculate: Payment from a principal · Principal (present value) 100,000 · Annual interest rate 5 % · Term 20 years · Payments per year: monthly (12) · Payment timing: ordinary annuity (end of period) → Result: Payment = 659.96 per period (240 payments). Source: Brealey/Myers/Allen: Principles of Corporate Finance, chapter “How to value annuities”; presentation of the formulas (ordinary annuity, annuity due): Wikipedia “Annuity”. Updated: .
How it is calculated
An annuity is a series of equal payments made at equal intervals – for instance a monthly income drawn from a lump sum, or a fixed regular contribution. Three quantities are linked: the present value (what the payments are worth today), the future value (what they grow to with interest) and the payment itself. Given two of them plus the rate and the term, the third can be calculated.
Formulas
With the periodic rate i = annual rate ÷ payments per year and n payments, an ordinary annuity has: present value = payment × (1 − (1 + i)^−n) ÷ i and future value = payment × ((1 + i)^n − 1) ÷ i. Rearranged: payment = present value × i ÷ (1 − (1 + i)^−n). For an annuity due (payments at the start of each period) the present and future values are multiplied by (1 + i); the payment from a principal is divided by (1 + i) accordingly.
Worked example
100,000 principal, 5% interest, 20 years, monthly payments at the end of each month: i = 5% ÷ 12 = 0.41667%, n = 240. Payment = 100,000 × 0.0041667 ÷ (1 − 1.0041667^−240) = 659.96. Over the term 158,389.38 is paid out, of which 58,389.38 is interest. As an annuity due the payment drops to 657.22. Conversely, a payment of 500 under the same terms has a present value of 75,762.66 and a future value of 205,516.83.
- Ordinary annuities are the norm for loans and pensions; rent and many savings plans are paid in advance.
- The higher the rate, the larger the payment a principal can fund and the lower the present value of a fixed payment.
- A loan repayment is the same calculation: there the principal is the amount borrowed.
Frequently asked questions
How do you calculate an annuity payment?
Multiply the principal by the periodic rate and divide by 1 minus (1 + periodic rate) to the power of minus the number of payments. For 100,000, 5% and 240 monthly payments that is 659.96.
What is the difference between an ordinary annuity and an annuity due?
An annuity due pays at the start of each period, an ordinary annuity at the end. Every payment moves one period earlier, which changes the interest; in the example the payment is 657.22 instead of 659.96.
What does the present value of an annuity tell me?
It is today’s value of all future payments. 240 monthly payments of 500 are worth 75,762.66 today at 5%, although 120,000 is paid in total.
Does this work for an insurance annuity?
Only as an approximation for a fixed-term annuity. Lifetime annuities also price in life expectancy and charges, which are not part of this calculation.
Sources and legal basis
- Brealey/Myers/Allen: Principles of Corporate Finance, chapter “How to value annuities”; presentation of the formulas (ordinary annuity, annuity due): Wikipedia “Annuity”
- Wikipedia – Rentenrechnung (present value of an annuity, future value of an annuity, annuity-due and ordinary annuity)
As of: · Editorial policy
Related tools
- Present Value CalculatorPresent value calculator: what is a future amount or a stream of payments worth today? Handles lump sums, annuities and perpetuities, with a rate comparison.
- Future value calculatorFuture value calculator: final value from a starting amount, interest and regular deposits – or the present value of a future sum. With formula and table.
- Financial Calculator (TVM Solver)Financial calculator for time value of money: enter four of N, I/Y, PV, PMT and FV and solve for the fifth, with payments at the end or beginning, with working.
- Retirement Withdrawal CalculatorRetirement withdrawal calculator: how long does your savings last with monthly withdrawals, return and inflation? Or what can you withdraw? With yearly table.
- Loan calculatorLoan calculator for monthly payment, total interest and payoff time on personal, car or home loans – with extra payments and an amortization schedule.
- Compound interest calculatorCompound interest calculator with monthly contributions: final balance, interest earned, inflation-adjusted value, time to reach a goal, chart and yearly table.
- Mortgage calculatorMortgage calculator: monthly payment with taxes, insurance, PMI and HOA from home price, down payment and rate – extra payments, 15 vs 30 years, amortization.
- Bond yield calculatorBond yield calculator: work out the yield to maturity from price, coupon and term – or the fair price from a yield – with duration and payment schedule.
- SSI calculator 2026 (Supplemental Security Income)SSI calculator 2026: your monthly federal SSI payment after income exclusions – $994 for one person, $1,491 for a couple, with housing help and work income.