Future Value of an Annuity

What Is the Future Value of an Annuity?

The future value of an annuity is the value of a group of recurring payments at a certain date from here on out, assuming a specific rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.

Figuring out the Future Value of an Annuity

Due to the time value of money, money received or paid out today is worth more than a similar amount of money will be from here on out. That is on the grounds that the money can be invested and permitted to develop after some time. By a similar logic, a lump sum of $5,000 today is worth in excess of a series of five $1,000 annuity payments spread out north of five years.

Ordinary annuities are more normal, yet an annuity due will bring about a higher future value, all else being equivalent.

Illustration of the Future Value of an Annuity

The formula for the future value of a ordinary annuity is as per the following. (An ordinary annuity pays interest toward the finish of a specific period, as opposed to toward the beginning, similarly as with a annuity due.)
$\begin &\text = \text \times \frac { \big ( (1 + r) ^ n - 1 \big ) } \ &\textbf \ &\text = \text \ &\text = \text \ &r = \text{Interest rate (also known as discount rate)} \ &n = \text \ \end$
For instance, assume somebody chooses to invest $125,000 each year for the next five years in an annuity they hope to compound at 8% each year. The expected future value of this payment stream utilizing the above formula is as per the following:
$\begin \text &= $125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \ &= $733,325 \ \end$
With an annuity due, where payments are made toward the beginning of every period, the formula is marginally unique. To track down the future value of an annuity due, essentially duplicate the formula above by a factor of (1 + r). So:
$\begin &\text = \text \times \frac { \big ( (1 + r) ^ n - 1 \big ) } \times ( 1 + r ) \ \end$
On the off chance that a similar model as above were an annuity due, its future value would be calculated as follows:
$\begin \text &= $125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \times ( 1 + 0.08 ) \ &= $791,991 \ \end$
All else being equivalent, the future value of an annuity due will be greater than the future value of an ordinary annuity since it has had an extra period to amass compounded interest. In this model, the future value of the annuity due is $58,666 more than that of the ordinary annuity.

Features

• Conversely, the current value of an annuity measures how much money will be required to deliver a series of future payments.
• In an ordinary annuity, payments are made toward the finish of each settled upon period. In an annuity due, payments are made toward the beginning of every period.
• The future value of an annuity is an approach to computing how much money a series of payments will be worth at one point from here on out.