Annuity Calculator
Free Annuity Calculator for financial & business math. Enter values to get step-by-step solutions with formulas and graphs.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
FV = PMT x ((1 + r)^n - 1) / r
Where FV = Future Value, PMT = periodic payment amount, r = periodic interest rate (annual rate divided by periods per year), and n = total number of payment periods. For an annuity due, multiply by (1 + r). The present value formula is PV = PMT x (1 - (1 + r)^(-n)) / r.
Worked Examples
Example 1: Retirement Savings Annuity
Problem:You contribute $500 per month for 30 years at 6% annual return. What is the future value?
Solution:Using FV = PMT x ((1 + r)^n - 1) / r\nPMT = $500, r = 0.06/12 = 0.005, n = 360\nFV = 500 x ((1.005)^360 - 1) / 0.005\nFV = 500 x (6.02258 - 1) / 0.005\nFV = 500 x 1,004.52 = $502,257
Result:Future Value: $502,257 | Total Contributed: $180,000 | Interest Earned: $322,257
Example 2: Present Value of Pension Payments
Problem:A pension pays $2,000 per month for 20 years. At 4% discount rate, what is the present value?
Solution:Using PV = PMT x (1 - (1 + r)^(-n)) / r\nPMT = $2,000, r = 0.04/12 = 0.003333, n = 240\nPV = 2,000 x (1 - (1.003333)^(-240)) / 0.003333\nPV = 2,000 x (1 - 0.4512) / 0.003333\nPV = 2,000 x 164.65 = $329,300
Result:Present Value: $329,300 | Total Payments: $480,000 | Interest Component: $150,700
Frequently Asked Questions
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity makes payments at the end of each period, while an annuity due makes payments at the beginning. This seemingly small timing difference has a meaningful impact on the final value. Because annuity due payments are made earlier, each payment has one additional period to earn interest, making the future value higher. The future value of an annuity due equals the ordinary annuity future value multiplied by (1 + r), where r is the periodic interest rate. Rent payments are a common example of an annuity due, while bond coupon payments typically follow the ordinary annuity pattern.
How is the future value of an annuity calculated?
The future value of an ordinary annuity uses the formula FV = PMT multiplied by ((1 + r)^n - 1) / r, where PMT is the periodic payment, r is the periodic interest rate, and n is the total number of periods. For an annuity due, you multiply the result by (1 + r) to account for the extra compounding period. This formula assumes equal payments at regular intervals and a constant interest rate throughout the term. The future value tells you how much your series of payments will be worth at the end of the annuity term after accounting for compound interest growth.
What is the present value of an annuity?
The present value of an annuity is the current lump sum that would be equivalent to receiving a series of future payments, discounted at a specific interest rate. It answers the question: how much would you need to invest today to generate a certain stream of payments? The formula is PV = PMT multiplied by (1 - (1 + r)^(-n)) / r. This concept is fundamental in finance for pricing bonds, valuing pension obligations, evaluating structured settlements, and determining fair loan amounts. A higher discount rate reduces the present value because future money is worth less.
How do interest rates affect annuity values?
Interest rates have a significant and opposite effect on future value versus present value of annuities. Higher interest rates increase the future value because each payment earns more interest over time, leading to greater compounding. Conversely, higher rates decrease the present value because future payments are discounted more heavily. For example, a 20-year annuity of $1,000 per month at 4% has a future value of about $366,774, but at 8% it grows to approximately $589,020. Understanding this relationship is critical for retirement planning, as even small rate changes compound dramatically over decades.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy