Annuity Calculator (Annual Rent)

An annuity is a series of equal payments made at regular intervals over a fixed period. Common examples include pension payouts, insurance premiums, lease instalments and bond coupon payments. The time value of money means a future payment is worth less than the same payment today.

In an ordinary annuity payments are made at the end of each period (e.g. month or year). In an annuity due payments are made at the beginning of each period. The annuity due is worth more because each payment is discounted one fewer period, so its present and future values are higher by a factor of (1 + r).

PV of an ordinary annuity = R × (1 − (1 + r)^−n) / r, where R is the periodic payment, r is the interest rate per period and n is the number of periods. For an annuity due, multiply by (1 + r). When the interest rate is zero, PV = R × n.

FV of an ordinary annuity = R × ((1 + r)^n − 1) / r. This represents the accumulated value of all payments at the end of the annuity term, assuming each payment earns interest until that point. For an annuity due multiply by (1 + r).

Use the annual interest rate that matches the payment frequency. If your payments are annual and the annual rate is 5%, enter 5%. If payments are monthly, use the monthly rate (annual rate / 12) and set the number of periods to months. The calculator defaults to an annual rate with annual payments.

The PV annuity factor (also called the present value interest factor of an annuity, PVIFA) is the multiplier applied to the payment to get the present value: PVIFA = (1 − (1+r)^−n) / r. Multiplying PVIFA by any payment amount gives the PV without repeating the full calculation.

An annuity has a fixed, finite number of payments. A perpetuity is an annuity that pays forever. The present value of a perpetuity is simply R / r (payment divided by interest rate). Common examples of perpetuities include certain government bonds and preferred stock dividends.

A fixed-rate loan or mortgage is mathematically an annuity from the lender's perspective. The PV formula determines the loan amount for given monthly payments, rate and term. Rearranging the formula gives the periodic payment: R = PV × r / (1 − (1+r)^−n), which is used in mortgage calculators.

Yes. If you make equal deposits each year into a savings account at a fixed interest rate, the future value of those deposits equals the FV of an annuity. Enter your annual deposit as the payment, your expected annual return as the rate, and the number of years to see how much you will accumulate.

The results are mathematically precise to standard double-precision floating point arithmetic, rounded to 2 decimal places for display. The formulas follow the international finance standard. Differences from bank statements may arise from different compounding conventions (e.g. daily vs. monthly vs. annual compounding).