# What Is It, Formula, and Calculation

Contents

## What Is the Future Worth of an Annuity?

The longer term worth of an annuity is the worth of a bunch of recurring funds at a sure date sooner or later, assuming a selected fee of return, or low cost fee. The upper the low cost fee, the higher the annuity’s future worth. So long as the entire variables surrounding the annuity are recognized equivalent to fee quantity, projected fee, and variety of intervals, it’s attainable to calculate the long run worth of the annuity.

### Key Takeaways

- The longer term worth of an annuity is a approach of calculating how a lot cash a sequence of funds can be value at a sure level sooner or later.
- Against this, the current worth of an annuity measures how a lot cash can be required to supply a sequence of future funds.
- In an abnormal annuity, funds are made on the finish of every agreed-upon interval. In an annuity due, funds are made initially of every interval.
- To calculate the long run worth of an annuity, you need to know the annuity fee quantity, variety of intervals, and projected fee of return.
- As a result of annuity due funds typically entail having a further compounding interval, the long run worth of an annuity due will often be increased than the long run worth of an annuity.

## Understanding the Future Worth of an Annuity

Due to the time worth of cash, cash acquired or paid out immediately is value greater than the identical amount of cash can be sooner or later. That is as a result of the cash may be invested and allowed to develop over time. By the identical logic, a lump sum of $5,000 immediately is value greater than a sequence of 5 $1,000 annuity funds unfold out over 5 years.

###
Peculiar annuities are extra frequent, however an annuity due will end in a better future worth, all else being equal.

Peculiar annuities are extra frequent, however an annuity due will end in a better future worth, all else being equal.

## System and Calculation of the Future Worth of an Annuity

The components for the long run worth of an abnormal annuity is as follows. (An abnormal annuity pays curiosity on the finish of a selected interval, quite than initially, as is the case with an annuity due.)

$$

P

=

PMT

×

(

(

1

+

r

)

n

−

1

)

r

the place:

P

=

Future worth of an annuity stream

PMT

=

Greenback quantity of every annuity fee

r

=

Curiosity fee (additionally recognized as low cost fee)

n

=

Quantity of intervals in which funds will be made

beginaligned &textP = textPMT occasions frac huge ( (1 + r) ^ n – 1 huge ) r &textbfwhere: &textP = textFuture worth of an annuity stream &textPMT = textDollar quantity of every annuity fee &r = textInterest fee (also referred to as low cost fee) &n = textNumber of intervals through which funds can be made endaligned

P=PMT×r((1+r)n−1)the place:P=Future worth of an annuity streamPMT=Greenback quantity of every annuity feer=Curiosity fee (additionally recognized as low cost fee)n=Quantity of intervals in which funds will be made

### Future Worth of an Annuity Due

With an annuity due, the place funds are made initially of every interval, the components is barely completely different. To search out the long run worth of an annuity due, merely multiply the components above by an element of (1 + r). So:

$$

P

=

PMT

×

(

(

1

+

r

)

n

−

1

)

r

×

(

1

+

r

)

beginaligned &textP = textPMT occasions frac huge ( (1 + r) ^ n – 1 huge ) r occasions ( 1 + r ) endaligned

P=PMT×r((1+r)n−1)×(1+r)

## Future Worth of an Annuity Instance

Assume somebody decides to take a position $125,000 per yr for the following 5 years in an annuity they anticipate to compound at 8% per yr. On this instance, the sequence of funds is a daily annuity through which the funds are made on the finish of every interval. The anticipated future worth of this fee stream utilizing the above components is as follows:

$$

Future worth

=

$

125

,

000

×

(

(

1

+

0.08

)

5

−

1

)

0.08

=

$

733

,

325

beginaligned textFuture worth &= $125,000 occasions frac huge ( ( 1 + 0.08 ) ^ 5 – 1 huge ) 0.08 &= $733,325 endaligned

Future worth=$125,000×0.08((1+0.08)5−1)=$733,325

### Future Worth of an Annuity Due

Assume the identical instance as above was an annuity due. This implies every of the $125,000 funds was made initially of every interval. Its future worth can be calculated as follows:

$$

Future worth

=

$

125

,

000

×

(

(

1

+

0.08

)

5

−

1

)

0.08

×

(

1

+

0.08

)

=

$

791

,

991

beginaligned textFuture worth &= $125,000 occasions frac huge ( ( 1 + 0.08 ) ^ 5 – 1 huge ) 0.08 occasions ( 1 + 0.08 ) &= $791,991 endaligned

Future worth=$125,000×0.08((1+0.08)5−1)×(1+0.08)=$791,991

All else being equal, the long run worth of an annuity due can be higher than the long run worth of an abnormal annuity as a result of it has had an additional interval to build up compounded curiosity. On this instance, the long run worth of the annuity due is $58,666 greater than that of the abnormal annuity.

## What Is a Future Worth Issue?

When calculating future values, one element of the calculation is known as the long run worth issue. The longer term worth issue is just the aggregated progress {that a} lump sum or sequence of money circulate will entail. For instance, if the long run worth of $1,000 is $1,100, the long run worth issue should have been 1.1. A future worth issue of 1.0 means the worth of the sequence can be equal to the worth immediately.

## What Is The Distinction Between Annuity and Annuity Due?

Annuity funds are sometimes made on the finish of a interval. An annuity due, nonetheless, is a fee made initially of a interval. Although it might not seem to be a lot of a distinction, there could also be appreciable variations between the 2 when contemplating what curiosity is accrued.

## What Is the Relationship Between Current Worth and Future Worth?

Current worth and future worth merely point out the worth of an funding trying ahead or trying again. The 2 ideas are instantly associated, as the long run worth of a sequence of money flows additionally has a gift worth. For instance, a gift worth of $1,000 immediately could also be equal to the long run worth of $1,200 immediately.

Most frequently, buyers and analysts will know one worth and attempt to remedy for the opposite. As an illustration, should you purchase a inventory immediately for $100 that awards a 2% dividend every year, you possibly can calculate the long run worth. Alternatively, if you wish to have $10,000 of future worth available for a down fee for a automobile subsequent yr, you possibly can remedy for the current worth.

## The Backside Line

An annuity is a sequence of funds revamped a time period, typically for a similar quantity every interval. Buyers can decide the long run worth of their annuity by contemplating the annuity quantity, projected fee of return, and variety of intervals. There are additionally implications whether or not the annuity funds are made initially of the interval or on the finish.