# Annuity Formula Explained

The easiest way to deal with an annuity formula is to use an annuity calculator to determine the amount of money youâ€™ll receive based on investments made over time. However, itâ€™s a good idea to understand the annuity formula used by the calculator in order to have a better idea of what you can expect from your investment over time. The annuity formula calculates income derived from an annuity plan over the duration of the contract. The period of time that your annuity will be in force is determined by an annuity formula, which can also provide an accurate estimate of how an annuity will perform over time. These factors are critical to the financial planning process.

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## The Future Value of an Annuity

An annuity plan provides a series of payments made at regular intervals. The future value of an annuity (FVoA) is the amount of money you can expect to receive in the future as investments are impacted by a promised rate of interest. The FVoA is obtained by finding the future value of every payment over the investment period and calculating the results.

## The Time Value of Money Concept

Annuity formulas consider the time value of money. What this means is that if you make a deposit of \$100 to an interest-bearing account today, that initial investment will be worth more in the future than it is today because it will have accrued the interest over time. In the formula representing this concept, your \$100 investment has both a present value (PV) and a future value (FV). The difference between these values is known as the return on investment (ROI).

## Examples

To determine the future value (FV) of that current \$100 (PV), you need to know the present value, the interest rate that your annuity will earn, and the length of time that \$100 will be held in the account.

If you invest your \$100 for a period of five years and receive an interest rate of five percent that is compounded annually, the Present Value of this money is \$105, or \$100 plus five percent interest. If you calculate this value for the five years the money will be in the account, your total at the end of that time â€“ the Future Value of your initial investment â€“ is \$127.63. The formula used in this calculation is

Future Value (FV) = Present Value (1+ the interest rate) to the power of n (the period of time your money is held in an annuity account.

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