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Tuesday, January 25, 2022

# Present Value of an Annuity Definition

## What Is Current Worth of an Annuity?

The current worth of an annuity is the present worth of futureÂ funds from an annuity, given a specified fee of return, or discount rate. The upper theÂ low costÂ 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.

## 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

Ã—

1

âˆ’

(

1

(

1

+

r

)

n

)

r

the place:

P

=

CurrentÂ worthÂ ofÂ anÂ annuityÂ stream

PMT

=

GreenbackÂ quantityÂ ofÂ everyÂ annuityÂ fee

r

=

CuriosityÂ feeÂ (additionallyÂ identifiedÂ asÂ low costÂ fee)

n

=

QuantityÂ ofÂ durationsÂ inÂ whichÂ fundsÂ willÂ beÂ 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

â€‹P=PMTÃ—r1âˆ’((1+r)n1â€‹)â€‹the place:P=CurrentÂ worthÂ ofÂ anÂ annuityÂ streamPMT=GreenbackÂ quantityÂ ofÂ everyÂ annuityÂ feer=CuriosityÂ feeÂ (additionallyÂ identifiedÂ asÂ low costÂ fee)n=QuantityÂ ofÂ durationsÂ inÂ whichÂ fundsÂ willÂ beÂ madeâ€‹

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:

CurrentÂ worth

=

$50 , 000 Ã— 1 âˆ’ ( 1 ( 1 + 0.06 ) 25 ) 0.06 =$

639

,

168

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

CurrentÂ worthâ€‹=$50,000Ã—0.061âˆ’((1+0.06)251â€‹)â€‹=$639,168â€‹

50

,

000

Ã—

1

âˆ’

(

1

(

1

+

0.06

)

25

)

0.06

Ã—

(

1

+

.

06

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=

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