Calculate present value, future value, periodic payment or interest rate for ordinary annuities and annuities due. Includes growing annuity support.
An annuity is a series of equal payments made at regular intervals over a fixed number of periods. The present value is the lump sum today that is equivalent to the full payment stream discounted at the given rate. The future value is the accumulated value of all payments at the end of the final period, including compound interest earned throughout.
Each payment in an annuity due is received one period earlier than the corresponding payment in an ordinary annuity. Since time value of money principles hold that money available earlier is worth more, every payment in an annuity due is worth more in present value terms. Mathematically, the annuity due PV equals the ordinary annuity PV multiplied by (1 + r). Rent payments are a classic annuity due — paid at the start of each month. Bond coupon payments are ordinary annuities — received at the end of each period.
A growing annuity is a payment stream where each payment increases by a fixed percentage each period. Growing annuities are used to model inflation-linked income streams such as pension payments rising with inflation, rental income on leases with annual rent review clauses, and salary-linked cash flows. The formula breaks down when the growth rate equals the discount rate (division by zero).
Payment frequency changes the number of compounding periods and the rate per period. An annual rate of 6% equates to a monthly rate of 0.5%, a quarterly rate of 1.5%, or a semiannual rate of 3%. This calculator uses the rate per period as entered, so ensure the rate you input matches the frequency selected. If your annuity has a 6% annual rate and monthly payments, enter 0.5 as the rate (6 divided by 12) and the total number of months as the periods.