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Difference between annuity and perpetuity


One of the universally accepted facts is that money has a value over time, that is, a rupee has a higher value today, than a year later. The temporary value of money is useful for determining the value of financial assets. There are two techniques used in this context, that is, annuity and perpetuity. Annuity It can be defined as a series of cash flows, usually of a fixed amount, paid / received at regular intervals. The interval can be annual, semiannual or quarterly, monthly, etc.

PerpetuityOn the other hand, it is a type of annuity that continues for an infinite number of years. It is also known as perpetual annuity.

In other words, annuity has a definite end, but Perpetuity never ends, it is undefined. After a deep analysis of the two methods, we have compiled the differences between annuity and perpetuity, to help you understand the two terms quickly and clearly.

Comparative graph

Basis for comparison Annuity Perpetuity
SenseA chain of regular cash flows up to a certain period of time is known as annuity.A series of cash outflows that occurs forever is known as Perpetuity.
TermSpecifiedEndless
PaymentDone or ReceivedFact
Future valueIt can be calculated with the help of the composition.It cannot be calculated.
ExampleLife insurance premium per year.Dividend of irredeemable preferred shares.

Annuity Definition

Constant periodic cash flows, over a specific period, are known as annuities. Cash flows can be receipts or disbursements of equal amounts made in an established time interval, that is, weekly, monthly, quarterly, semiannual or annual. The following are the types of annuity:

  • Ordinary Annuity: Payment or cash deposit occurs in the year.
  • Annuity due: Cash inflow or outflow occurs at the beginning.
  • Perpetuity: The annuity that is eternal.
  • Others: Some other types of annuities are fixed annuities and variable annuities.

Formula:

Where, n = number of years R = Return rate

Examples: Payment of credit to the bank for recurring deposit.

Definition of Perpetuity

An indefinite series of payments of equal amounts at regular intervals on a fixed date is known as Perpetuity. The word 'Perpetuity' is a combination of two terms of perpetual annuity, that is, a form of annuity that is maintained forever and, therefore, its future value cannot be calculated. Therefore, it is a continuous flow of consistent cash flows over the years.

First and foremost, the initial fund, that is, capital, is established and then payments flow from the funds for an infinite period. These fixed cash flows are annual interest payments. They start on a certain date and last forever. Perpetuality is divided into two categories:

  • Constant perpetuality : remains constant throughout the years.
  • Increasing Perpetuity: It grows at a uniform rate forever.

Formula:

Where, C = Cash flow, that is, interest or dividends R = interest rate G = growth rate

Example: Scholarships paid to the endowment fund.

Key differences between annuity and perpetuity

The following are the main differences between annuity and perpetuity:

  1. A series of continuous cash flows of an equal amount over a limited period is known as annuity. Perpetuality is a type of annuity that continues forever.
  2. The annuity is for a fixed period, but Perpetuity is eternal.
  3. In an annuity, payment is made or received. On the contrary, in perpetuity, there is only cash outflow.
  4. The future value of the annuity can be easily calculated, which is not possible in the case of Perpetuity.
  5. Perpetuality is an annuity, but an annuity is not perpetuity.

Conclusion

The temporary value of money says that the value of a rupee in the present will be changed in the future. To calculate the value of financial assets such as stocks, bonds, obligations and bank deposits, the methods of annuity and perpetuity are used. Traditional annuities, pension payments, mortgage payments are an example of an annuity that give uniform and predictable returns for a limited number of years. On the other hand, lease rentals, corporate stock dividends are examples of perpetuity.

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