Formula for the Life of an Annuity With Payouts

Formula for the Life of an Annuity With Payouts
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Annuities are useful tools for a variety of investing and saving scenarios, but understanding how they work and how much they will pay can be challenging. The present value of an annuity, according to the website AccountingCoach, is "Future amounts that have been discounted to the present." You may also calculate the future value of an annuity, however, to determine its worth as it pays out over time.

Annuity Basics

An annuity is a financial product that delivers a series of payment at fixed intervals for a period of time. Annuities last for a set number of years or until the owner, known as an annuitant, is no longer living. For the life of the annuity, it makes payouts while continuing to gain value from interest. Because annuities are similar to other types of investments and savings products, it is useful to calculate their future values to compare options using relevant data.

Types of Annuities

There are two major types of annuities with different calculation requirements to determine future value. The first is an ordinary annuity, also known as an annuity in arrears. This type of annuity makes payments at the end of each period. An annuity due, by contrast, issues payments as each payment period begins. Because money in an annuity grows over time, the timing of these payments has an impact on the value of the annuity.

Ordinary Annuity Formula

To determine the future value of an ordinary annuity with payouts you'll need several pieces of data. They include the annuity's interest rate per payment period, which the formula represents as "i," as well as the number of periods left for the annuity. For an annuity with a fixed number of periods this is straightforward. However, for a life annuity, you'll need to estimate the number of periods in the expected lifetime of the annuitant. The number of periods is represented as "n." The future value of the ordinary annuity is equal to the amount of each payment times the quantity:

((1 + i)n - 1) / i.

Annuity Due Formula

The future value of an annuity due is similar to the future value of an ordinary annuity. However, each payment arrives one period earlier. Using the same data, you must first calculate the future value of the annuity as if it were an ordinary annuity. To account for the earlier payment, multiply the result by (1 + i). This means that an annuity with the same number of periods, same interest rate and same payment amount will have a slightly higher future value as it pays out if it is an annuity due.