What is the future value of an annuity formula?

FV = PMT × ((1 + r)^n − 1) ÷ r. PMT is the payment per period, r the rate per period as a decimal, n the number of payments. Multiply by (1 + r) for annuity-due.

What is the present value of an annuity formula?

PV = PMT × (1 − (1 + r)^−n) ÷ r. This is the lump sum that would today exactly buy a stream of n payments of PMT discounted at rate r per period. Multiply by (1 + r) for annuity-due.

What is the difference between an ordinary annuity and an annuity-due?

Ordinary annuities pay at the END of each period (most loans, bonds, dividends). Annuities-due pay at the START (most rent, lease, and insurance premiums). Annuity-due is the ordinary formula × (1 + r).

How do I convert an annual rate to a per-period rate?

Divide by the number of payments per year. For monthly payments divide the annual rate by 12; quarterly by 4; semi-annual by 2.

When the rate is zero, both FV and PV reduce to PMT × n — payments without interest. The calculator handles this case so it does not divide by zero.

Is anything sent to a server?

No. All annuity math runs in your browser; nothing is uploaded.

Annuity Calculator

Compute present or future value of an ordinary annuity or annuity-due payment stream.

Written by Golam Rabbani, Founder & Lead Engineer

This interactive tool requires JavaScript. Read the formula and worked example below; you can compute the result by hand.

How to use this annuity calculator

Pick "Future value of annuity" to accumulate a payment stream, or "Present value of annuity" to discount it.
Enter the payment per period (PMT) and pick a currency.
Type the rate per period as a percent — divide an annual rate by payments-per-year.
Type the number of payments (n).
Pick payment timing: end of period (ordinary annuity) or start (annuity-due).
Press Calculate to see the value, total payments, and implied interest.

About this annuity calculator

An annuity is a fixed series of equal payments at equal intervals. The calculator implements the four standard time-value-of-money formulas. Future value of an ordinary annuity: FV = PMT × ((1 + r)^n − 1) ÷ r. Present value of an ordinary annuity: PV = PMT × (1 − (1 + r)^−n) ÷ r. For an annuity-due (payments at the start of each period) both formulas are multiplied by (1 + r). These are the formulas in the CFA Institute Time-Value-of-Money curriculum and the U.S. SEC's Investor.gov "Annuities" investor publication.

Worked example: PMT = USD 250 paid at the end of every month, r = 0.5% per month, n = 240 (20 years). Future value: FV = 250 × ((1.005)^240 − 1) ÷ 0.005 ≈ USD 115,510.31. Present value of the same stream: PV = 250 × (1 − (1.005)^−240) ÷ 0.005 ≈ USD 34,896.07. Total paid over 20 years = 250·240 = USD 60,000. For FV, interest earned ≈ USD 55,510.31; for PV, the discount captures USD 60,000 − 34,896.07 ≈ USD 25,103.93 of time-value erosion. Currency is a label only; there is no exchange-rate lookup.

FAQ

What is the future value of an annuity formula?: FV = PMT × ((1 + r)^n − 1) ÷ r. PMT is the payment per period, r the rate per period as a decimal, n the number of payments. Multiply by (1 + r) for annuity-due.
What is the present value of an annuity formula?: PV = PMT × (1 − (1 + r)^−n) ÷ r. This is the lump sum that would today exactly buy a stream of n payments of PMT discounted at rate r per period. Multiply by (1 + r) for annuity-due.
What is the difference between an ordinary annuity and an annuity-due?: Ordinary annuities pay at the END of each period (most loans, bonds, dividends). Annuities-due pay at the START (most rent, lease, and insurance premiums). Annuity-due is the ordinary formula × (1 + r).
How do I convert an annual rate to a per-period rate?: Divide by the number of payments per year. For monthly payments divide the annual rate by 12; quarterly by 4; semi-annual by 2.
What if r = 0?: When the rate is zero, both FV and PV reduce to PMT × n — payments without interest. The calculator handles this case so it does not divide by zero.
Is anything sent to a server?: No. All annuity math runs in your browser; nothing is uploaded.