PV of Perpetuity
Present Value of Perpetuity
Perpetuity is an infinite series of periodic payments of equal face value. In other words, perpetuity is a situation where a constant payment is to be made periodically for an infinite amount of time. It as an annuity having no end and that is why the perpetuity is sometimes called as perpetual annuity.
Although the total face value of perpetuity is infinite and undeterminable, its present value is not. According to the time value of money principle, the present value of perpetuity is the sum of the discounted value of each periodic payment of the perpetuity. Present value of perpetuity is finite because the discounted value of far future payments of the perpetuity reduces considerably and reaches close to zero.
The following formula is used to calculate the present value of perpetuity:
Present Value (PV) of Perpetuity =&A
Where,&&&A is the fi and&&&r is the interest rate or discount rate per compounding period.
Example 1: Calculate the present value on Jan 1, 20X0 of a perpetuity paying $1,000 at the end of each month starting from January 20X0. The monthly discount rate is 0.8%.
Periodic Payment
Discount Rate
Present Value
= $1,000 & 0.8%
= $125,000
Written byPerpetuity | Definition of Perpetuity by Merriam-Webster
per·pe·tu·i·ty
\?p?r-p?-'tü-?-tē, -'tyü-\
: the state of continuing forever or for a very long time
Source: Merriam-Webster's Learner's Dictionary
Full Definition of perpetuity
perpetuities
the quality or state of being
&bequeathed to them in perpetuity&3 a
the condition of an estate limited so that it will not take effect or vest within the period fixed by law b
an estate so limited4
an annuity payable forever
defined for English-language learners
defined for kids
Examples of perpetuity in a sentence
&lands that should remain in their wild state in perpetuity&
Did You Know?
Continual existence—that elusive concept has made perpetuity a favorite term of philosophers and poets for centuries. The word derives ultimately from the Latin adjective perpetuus ("continual" or "uninterrupted"), which is also the source of our perpetual and perpetuate. It frequently occurs in the phrase "in perpetuity," which essentially means "forever" or "for an indefinitely long period of time." Perpetuity also has some specific uses in law. It can refer to an arrangement in a will rendering land forever
(or at least, for a period longer than is set by rules against such arrangements) or to an annuity that is payable forever.
Origin and Etymology of perpetuity
Middle English perpetuite, from Anglo-French perpetuité, from Latin perpetuitat-, perpetuitas, from perpetuus
First Known Use: 15th century
perpetuity Synonyms
Synonyms , , See more at
Law Dictionary
per·pe·tu·i·ty
\?p?r-p?-'tü-?-tē, -'tyü-\
perpetuities
the quality, state, or duration of being perpetual &devised to them in perpetuity& 2a
the condition of a future estate limited in such a way as not to vest within the period fixed by law for the
a limitation that gives rise to such a situation b
an estate that will not vest within the period fixed by law
— see also ,
an annuity payable forever
Phrases related to PERPETUITY
Related Phrases
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a descendant of a wealthy family
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state of being perpetual
unlimited time
Concept Thesaurus for word perpetuity
1. ABSOLUTE TIME
Synonyms - noun
Synonyms - verbs
Synonyms - adjectives
Synonyms - phrases
labitur et labetur in omne volubilis oevum [Horace]; "but thou shall flourish in immortal youth" [Addison]; "Eternity! thou pleasing, dreadful thought" [Addison]; "her immortal part with angels lives" [Romeo & Juliet]; ohne Rast [Goethe's motto "without rest" (German)];
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Roget's 21st Century Thesaurus, Third Edition Copyright (C) 2013 by the Philip Lief Group.
Word Origin & History
perpetuity c.1400; see perpetual.
Example Sentences for perpetuity
Whether or no that income was hers in perpetuity, or only for life, he had not positively known when he made his offer.
What, therefore, consists with the perpetuity and strength of the Union?
The peshkash or tribute payable to government in perpetuity amounts to about 330,000 a year.
What is the security of a tomb or the perpetuity of an embalmment?
For it was this belief in its own perpetuity that was its strength and weakness.
Nor is this conflict, nor is its perpetuity, difficult of explanation.
In memory of this event, the Hamor gate, through which the enemy had been admitted, was walled up in perpetuity.
Its perpetuity is linked closely with the resistance of all efforts at reform.
Japan and the whole world believed that the Liaotung Peninsula was made over to China in perpetuity.
Perpetuity of the state is synonymous with perpetuity of the race.Present Value of Growing Perpetuity
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Present Value of Growing Perpetuity
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The present value of a growing perpetuity formula is the cash flow after the first period divided by the difference between
the discount rate and the growth rate.
A growing perpetuity is a series of periodic payments that grow at a proportionate rate and are received for an infinite
amount of time. An example of when the present value of a growing perpetuity formula may be used is commercial real estate.
The rental cash flows could be considered indefinite and will grow over time.
It is important to note that the discount rate must be higher than the growth rate when using the present value of a
growing perpetuity formula. This is due to the present value of a growing perpetuity formula being an infinite geometric
series as explained in one of the following sections. In theory, if the growth rate is higher than the discount rate, the
growing perpetuity would have an infinite value.
Example of the Present Value of Growing Perpetuity Formula
An example of the present value of a growing perpetuity formula would be an annual cash flow of $1000 that will continue
indefinitely. This cash flow is expected to grow at 5% per year and the required return used for the discount rate is 10%. The
equation for this example of the present value of a growing perpetuity formula would be
which would return a present value of $20,000.
How the Present Value of Growing Perpetuity Formula is derived?
A growing perpetuity is a series of periodic payments that continue indefinitely and grow at a proportionate rate.
Therefore, the formula for the present value of a growing perpetuity can be shown as
This series will continue for an infinite amount of periods. This formula could be rewritten as
This is considered to be an infinite geometric series with a common ratio of (1+g)/(1+r).
Putting this formula into the infinite geometric series formula would result in
This formula could be shortened by multiplying it by (1+r)/(1+r), which is to multiply it by one.
This would result in
which could be further reduced to the present value of a growing perpetuity formula shown at the top of the page.
Formulas related to PV of Growing Perpetuity
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