# Present Value of an Annuity: Meaning, Formula, and Example

Contents

## What Is the Current Worth of an Annuity?

The current worth of an annuity is the present worth of future funds from an annuity, given a specified price of return, or low cost price. The upper the low cost price, the decrease the current worth of the annuity.

Current worth (PV) is a crucial calculation that depends on the idea of the time worth of cash, whereby a greenback in the present day is comparatively extra “helpful” by way of its buying energy than a greenback sooner or later.

### Key Takeaways

- The current worth of an annuity refers to how a lot cash can be wanted in the present day to fund a collection of future annuity funds.
- Due to the time worth of cash, a sum of cash obtained in the present day is value greater than the identical sum at a future date.
- You should use a gift worth calculation to find out whether or not you may obtain more cash by taking a lump sum now or an annuity unfold out over a lot of years.

#### Current Worth of an Annuity

## Understanding the Current Worth of an Annuity

An annuity is a monetary product that gives a stream of funds to a person over a time period, sometimes within the type of common installments. Annuities could be both quick or deferred, relying on when the funds start. Rapid annuities begin paying out instantly, whereas deferred annuities have a delay earlier than funds start.

Due to the time worth of cash, cash obtained in the present day is value greater than the identical sum of money sooner or later as a result of it may be invested within the meantime. By the identical logic, $5,000 obtained in the present day is value greater than the identical quantity unfold over 5 annual installments of $1,000 every.

Current worth is a crucial idea for annuities as a result of it permits people to check the worth of receiving a collection of funds sooner or later to the worth of receiving a lump sum fee in the present day. By calculating the current worth of an annuity, people can decide whether or not it’s extra helpful for them to obtain a lump sum fee or to obtain an annuity unfold out over a lot of years. This may be notably essential when making monetary selections, akin to whether or not to take a lump sum fee from a pension plan or to obtain a collection of funds from an annuity. Current worth calculations will also be used to check the relative worth of various annuity choices, akin to annuities with totally different fee quantities or totally different fee schedules.

### Current Worth and the Low cost Charge

The low cost price is a key consider calculating the current worth of an annuity. The low cost price is an assumed price of return or rate of interest that’s used to find out the current worth of future funds.

The low cost price displays the time worth of cash, which implies that a greenback in the present day is value greater than a greenback sooner or later as a result of it may be invested and doubtlessly earn a return. The upper the low cost price, the decrease the current worth of the annuity, as a result of the long run funds are discounted extra closely. Conversely, a decrease low cost price ends in the next current worth for the annuity, as a result of the long run funds are discounted much less closely.

Generally, the low cost price used to calculate the current worth of an annuity ought to replicate the person’s alternative price of capital, or the return they might count on to earn by investing in different monetary devices. For instance, if a person might earn a 5% return by investing in a high-quality company bond, they could use a 5% low cost price when calculating the current worth of an annuity. The smallest low cost price utilized in these calculations is the risk-free price of return. U.S. Treasury bonds are usually thought-about to be the closest factor to a risk-free funding, so their return is commonly used for this function.

It is essential to notice that the low cost price used within the current worth calculation will not be the identical because the rate of interest that could be utilized to the funds within the annuity. The low cost price displays the time worth of cash, whereas the rate of interest utilized to the annuity funds displays the price of borrowing or the return earned on the funding.

###
The other of current worth is future worth (FV). The FV of cash can be calculated utilizing a reduction price, however extends into the long run.

The other of current worth is future worth (FV). The FV of cash can be calculated utilizing a reduction price, however extends into the long run.

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

The system for the current worth of an atypical annuity, is under. An atypical annuity pays curiosity on the finish of a specific interval, fairly than originally:

$$

P

=

PMT

×

1

−

(

1

(

1

+

r

)

n

)

r

the place:

P

=

Current worth of an annuity stream

PMT

=

Greenback quantity of every annuity fee

r

=

Curiosity price (additionally identified as low cost price)

n

=

Quantity of durations in which funds will be made

beginaligned &textP = textPMT instances frac 1 – Massive ( frac 1 ( 1 + r ) ^ n Massive ) r &textbfwhere: &textP = textPresent worth of an annuity stream &textPMT = textDollar quantity of every annuity fee &r = textInterest price (often known as low cost price) &n = textNumber of durations by which funds will probably be made endaligned

P=PMT×r1−((1+r)n1)the place:P=Current worth of an annuity streamPMT=Greenback quantity of every annuity feer=Curiosity price (additionally identified as low cost price)n=Quantity of durations in which funds will be made

## Instance of the Current Worth of an Annuity

Assume an individual has the chance to obtain an atypical annuity that pays $50,000 per 12 months for the subsequent 25 years, with a 6% low cost price, or take a $650,000 lump-sum fee. Which is the higher possibility? Utilizing the above system, the current worth of the annuity is:

$$

Current worth

=

$

50

,

000

×

1

−

(

1

(

1

+

0.06

)

25

)

0.06

=

$

639

,

168

beginaligned textPresent worth &= $50,000 instances frac 1 – Massive ( frac 1 ( 1 + 0.06 ) ^ 25 Massive ) 0.06 &= $639,168 endaligned

Current worth=$5,×.61−((1+.6)251)=$639,168

Given this info, the annuity is value $10,832 much less on a time-adjusted foundation, so the particular person would come out forward by selecting the lump-sum fee over the annuity.

## Annuity vs. Annuity Due

An atypical annuity makes funds on the finish of every time interval, whereas an annuity due makes them originally. All else being equal, the annuity due will probably be value extra within the current. Within the case of an annuity due, since funds are made originally of every interval, the system is barely totally different. To search out the worth of an annuity due, merely multiply the above system by an element of (1 + r):

$$

P

=

PMT

×

1

−

(

1

(

1

+

r

)

n

)

r

×

(

1

+

r

)

beginaligned &textP = textPMT instances frac 1 – Massive ( frac 1 ( 1 + r ) ^ n Massive ) r instances ( 1 + r ) endaligned

P=PMT×r1−((1+r)n1)×(1+r)

So, if the instance above referred to an annuity due, fairly than an atypical annuity, its worth can be as follows:

$$

Current worth

=

$

50

,

000

×

1

−

(

1

(

1

+

0.06

)

25

)

0.06

×

(

1

+

.

06

)

=

$

677

,

518

beginaligned textPresent worth &= $50,000 instances frac 1 – Massive ( frac 1 ( 1 + 0.06 ) ^ 25 Massive ) 0.06 instances ( 1 + .06 ) &= $677,518 endaligned

Current worth=$50,000×0.061−((1+0.06)251)×(1+.06)=$677,518

On this case, the particular person ought to select the annuity due possibility as a result of it’s value $27,518 greater than the $650,000 lump sum.

## Why is Future Worth (FV) Necessary to buyers?

Future worth (FV) is the worth of a present asset at a future date primarily based on an assumed price of development. You will need to buyers as they will use it to estimate how a lot an funding made in the present day will probably be value sooner or later. This may assist them in making sound funding selections primarily based on their anticipated wants. Nonetheless, exterior financial components, akin to inflation, can adversely have an effect on the long run worth of the asset by eroding its worth.

## How Does Strange Annuity Differ From Annuity Due?

An atypical annuity is a collection of equal funds made on the finish of consecutive durations over a hard and fast size of time. An instance of an atypical annuity contains loans, akin to mortgages. The fee for an annuity due is made originally of every interval. A typical instance of an annuity due fee is hire. This variance in when the funds are made ends in totally different current and future worth calculations.

## What Is the System for the Current Worth of an Strange Annuity?

The system for the current worth of an atypical annuity is:

$beginaligned &textP = textPMT instances frac 1 – Massive ( frac 1 ( 1 + r ) ^ n Massive ) r &textbfwhere: &textP = textPresent worth of an annuity stream &textPMT = textDollar quantity of every annuity fee &r = textInterest price (often known as low cost price) &n = textNumber of durations by which funds will probably be made endaligned$

P=PMT×r1−((1+r)n1)the place:P=Current worth of an annuity streamPMT=Greenback quantity of every annuity feer=Curiosity price (additionally identified as low cost price)n=Quantity of durations in which funds will be made

## What Is the System for the Current Worth of an Annuity Due?

With an annuity due, by which funds are made originally of every interval, the system is barely totally different than that of an atypical annuity. To search out the worth of an annuity due, merely multiply the above system by an element of (1 + r):

$beginaligned &textP = textPMT instances frac 1 – Massive ( frac 1 ( 1 + r ) ^ n Massive ) r instances ( 1 + r ) endaligned$

P=PMT×r1−((1+r)n1)×(1+r)

## The Backside Line

The current worth (PV) of an annuity is the present worth of future funds from an annuity, given a specified price of return or low cost price. It’s calculated utilizing a system that takes into consideration the time worth of cash and the low cost price, which is an assumed price of return or rate of interest over the identical period because the funds. The current worth of an annuity can be utilized to find out whether or not it’s extra helpful to obtain a lump sum fee or an annuity unfold out over a lot of years.