What Is an Annuity Calculator?
This tool values a finite stream of equal payments at a constant rate. It can solve future value, present value, payment, nominal interest rate or whole payment periods. An insurance annuity is a contract with additional terms: this mathematical model does not value mortality guarantees, surrender charges, insurer credit risk or riders.
Choose the Cash-Flow Direction First
- Future Value: enter a regular deposit, nominal annual rate and whole periods. The schedule starts at zero and adds each deposit.
- Present Value: enter a regular payment and discount rate to find the equivalent balance today. The schedule then withdraws those payments from that balance.
- Payment: a positive present value solves repayment or withdrawals. Set present value to zero to reveal a future savings target; this assumes no initial deposit.
- Interest Rate: enter positive payment and present value plus whole periods. The solver searches 0%–100% per period and reports the equivalent nominal annual rate. It rejects unattainable or nonunique inputs.
- Periods: enter a balance, payment and nominal rate. The result rounds up to a whole interval, with a smaller final payment where necessary. A payment that cannot amortize the balance produces an error.
All modes support at most 1,200 periods. Choose monthly, quarterly, semiannual or annual payments. After Calculate, edits update the result; Clear hides it. Amounts use USD formatting but no currency conversion. No market-price request is made.
Ordinary Annuity and Annuity Due
Ordinary payments occur at period end; due payments occur at period start. A due deposit earns one additional period of interest. For a positive rate its present and future values exceed those of an ordinary stream with the same payment and period count. At zero interest they are equal.
Constructed example: three $100 deposits at 1% per period produce $303.01 at period three when paid at period ends, or $306.0401 when paid at period starts. These are mathematical inputs, not historical investment returns.
Annuity Formulas and Rate Conventions
Let P be the payment, n the whole period count and r the periodic rate. For an ordinary stream:
- FV = P × ((1 + r)^n − 1) / r.
- PV = P × (1 − (1 + r)^(-n)) / r.
- For due payments multiply either factor by 1 + r; divide the target value by the appropriate factor to solve payment.
- At r = 0, FV = PV = P × n. The implementation uses this limit instead of dividing by zero.
The entered nominal annual rate j becomes r = j / m, where m is payments per year and rates are decimals. Thus 6% nominal with monthly payments means 0.5% per month and approximately 6.1678% effective annually. A fee-inclusive APR should not replace the contract rate in this amortization formula. A savings product quoting an effective annual yield needs conversion first.
Read the Schedule Before Comparing Scenarios
The savings schedule earns interest on the existing balance and deposits at the selected time. A repayment schedule earns interest on the outstanding balance and subtracts payments; due payments reduce the balance before that period’s interest. The final payment is capped at the remaining amount owed. Totals sum the actual schedule.
The separate FV of Payment Stream is a future-value equivalent of those payments. It is not the remaining loan or withdrawal balance. Check the final schedule row for that balance. Rate mode separately labels nominal and effective annual rates, so the two figures are not mistaken for one another.
A fixed-payment loan can use this model when payment and compounding intervals coincide. Irregular first periods, daily interest, extra payments, variable rates, fees and balloon payments require a different cash-flow schedule. The tool does not calculate those adjustments or the legal disclosure APR.
What the Model Leaves Out
Retirement withdrawals can be illustrated at a constant assumed return, but real returns arrive in a sequence and can be negative. Inflation changes purchasing power; fees and taxes change cash available. An insurance contract may guarantee different benefits and impose surrender conditions. Compare those contract terms separately rather than treating this present value as a complete fair-value quote.
Primary references: CFPB on interest rate versus APR and SEC Investor.gov on insurance annuities and charges.