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Present Value of an Annuity Definition

What Is Current Worth of an Annuity?

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

Key Takeaways

  • The current worth of an annuity refers to how a lot cash could 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 will obtain more cash by taking a lump sum now or an annuity unfold out over various years.

Current Worth of an Annuity

Understanding Current Worth of an Annuity

Due to the time value of money, cash obtained in the present day is value greater than the identical amount of cash 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.

The future value of cash is calculated utilizing a reduction fee. The low cost fee refers to an rate of interest or an assumed fee of return on different investments over the identical length because the funds. The smallest low cost fee utilized in these calculations is the risk-free rate of return. U.S. Treasury bonds are usually thought-about to be the closest factor to a risk-free funding, so their return is usually used for this function.

Instance of Current Worth of an Annuity

The method for the current worth of an ordinary annuity, versus an annuity due, is under. (An abnormal annuity pays curiosity on the finish of a selected interval, moderately than firstly, as is the case with an annuity due.)

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 fee (additionally identified as low cost fee)

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 fee (also called low cost fee) &n = textNumber of durations by which funds can 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 fee (additionally identified as low cost fee)n=Quantity of durations in which funds will be made

Assume an individual has the chance to obtain an abnormal annuity that pays $50,000 per 12 months for the following 25 years, with a 6% low cost fee, or take a $650,000 lump-sum fee. Which is the higher possibility? Utilizing the above method, 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=$50,000×0.061((1+0.06)251)=$639,168

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

An abnormal annuity makes funds on the finish of every time interval, whereas an annuity due makes them firstly. All else being equal, the annuity due can be value extra within the current.

With an annuity due, by which funds are made firstly of every interval, the method is barely totally different. To search out the worth of an annuity due, merely multiply the above method 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, moderately than an abnormal annuity, its worth could 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 individual 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 based mostly on an assumed fee of development. You will need to buyers as they’ll use it to estimate how a lot an funding made in the present day can be value sooner or later. This may assist them in making sound funding selections based mostly 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 Peculiar Annuity Differ From Annuity Due?

An abnormal annuity is a collection of equal funds made on the finish of consecutive durations over a set size of time. An instance of an abnormal annuity consists of loans, akin to mortgages. The fee for an annuity due is made firstly of every interval. A typical instance of an annuity due fee is lease. This variance in when the funds are made leads to totally different current and future worth calculations.

What Is the System for the Current Worth of an Peculiar Annuity?

The method for the current worth of an abnormal annuity is:

P=PMT×1−(1(1+r)n)rthe place:P=Current worth of an annuity streamPMT=Greenback quantity of every annuity feer=Curiosity fee (additionally identified as low cost fee)n=Quantity of durations in which funds will be madebeginaligned &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 fee (also called low cost fee) &n = textNumber of durations by which funds can be made endalignedP=PMT×r1((1+r)n1)the place:P=Current worth of an annuity streamPMT=Greenback quantity of every annuity feer=Curiosity fee (additionally identified as low cost fee)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 firstly of every interval, the method is barely totally different than that of an abnormal annuity. To search out the worth of an annuity due, merely multiply the above method 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 ) endalignedP=PMT×r1((1+r)n1)×(1+r)

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