Difference Between Annuity and Perpetuity (With Table)

Annuity vs Perpetuity

The key difference between Annuity and Perpetuity lies in the fact that while annuity continues for a fixed period of time, perpetuity continues for an indefinite period of time.

The amount of money invested in both cases can be the same or different as per individual.

Without having a background in finance makes it difficult for a person to understand the terms used in the financial world.

We all are somehow, related to the financial sector and it becomes necessary for everyone to understand the basic terms of finance.

Annuity and Perpetuity are two of the most used financial terms. In simple words, Annuity is a fixed amount of periodic cash flow for a limited time or a series of the fixed amount paid or received on regular intervals (that can be annually, semi-annually, quarterly, monthly, etc.).

Perpetuity is a type of annuity that continuous for an indefinite period. Perpetuity is an infinite series of periodic payments of equal face value.

Let’s understand these two concepts deeply.


 

Comparison Table Between Annuity and Perpetuity (in Tabular Form)

Parameter of ComparisonAnnuityPerpetuity
MeaningAn Annuity is a fixed amount paid or received on equal intervals for a specific time.On the other hand, Perpetuity is an equal payment of an amount for an infinite period.
DurationAnnuity continuous for a fixed time.While the duration of perpetuity is infinite.
TypesThere are two types of Annuity-
1. Ordinary Annuity.
2. Annuity due.
Perpetuity doesn’t have any type.
Interest usedCompound interest is used for calculation of present value or future value of an Annuity.In the case of Perpetuity, Simple interest is used to calculate the present value.
Future valueFuture Value of an Annuity can be calculated, by using compound interest.While the Future Value of a Perpetuity cannot be calculated.

 

What is Annuity?

An Annuity is a series of the same amount of cash flow, paid or received on equal intervals of time for a predetermined time. An annuity is used for a variety of purposes, but the most common use of Annuity is for pension payment.

The areas where Annuity is commonly used are EMI’s, Life Insurance premiums, etc.

Compound interest is used for calculation of present value or future value of an Annuity.

Since Annuity is paid or received on fixed intervals like annually, semi-annually (6-months), quarterly (3-months), monthly, etc. the interest gets compounded as per the fixed period.

An annuity is mainly part of retirement plans and insurance contracts. Annuity generally have a few types but mainly it has two types-:

  1.  Annuity Due – The annuity payments or receipts are required to be made or gained at the beginning of the period, e.g. Rent paid in advance. 
  2.  Ordinary Annuity – the annuity payments or receipts are required to be made or gained at the end of each period, e.g. Coupon payments by a financial institution.
Types of Annuity 1
Types of Annuity
 

What is Perpetuity?

Perpetuity is a type of Annuity that never comes to an end. Perpetuity is also known as ‘Perpetual Annuity’ and the word ‘Perpetuity’ is derived by combining these two words, ‘Perpetual + Annuity’.

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Perpetuity is a series of cash flow that will be paid at regular intervals and for an infinite period.

The best example of Perpetuity is the bonds issued by the British Government in 1751 known as CONSOL, on which the government pays a steady form of interest forever as these bonds do not have a maturity date.

Since Perpetuity is a financial asset, therefore, its owner will receive constant amount forever. Since the time period is not fixed, compound interest cannot be used in fields where Perpetuity is concerned.

Also, the Principal is never repaid in the case of Perpetuity. Let’s understand perpetuity with this; when an owner purchases a property and then rents it out.

The owner is entitled to an infinite stream of cash flow from the renter as long as the property continues to exist (assuming the renter will rent).

Perpetuity do not have types but can be classified as-

  1. Constant Perpetuity – it is that Perpetuity, which remains the same forever.
  2. Growing Perpetuity – it grows at a uniform rate forever.
Perpetuity Calculation Formula
Perpetuity Calculation Formula

Main Differences Between Annuity and Perpetuity

  1. An annuity is paid or received for a fixed period. On the other hand, Perpetuity is paid for an indefinite time.
  2. The Future Value of an Annuity can be determined. But the Future Value of a Perpetuity cannot be calculated.
  3. Compound interest is used in the calculation of the present value of an annuity. Whereas in the case of Perpetuity compound interest has no use.
  4. An annuity is a wide concept since perpetuity is a type of Annuity.
  5. The annuity has more applications compared to Perpetuity, which has a limited application.
  6. In the case of Annuity, the payment can be made or received but in Perpetuity it is only made.
  7. Life insurance premiums, retirement plans, etc. often include Annuity. While bonds without a maturity date, long terms lease contracts, etc. includes the concept of Perpetuity. 

 

Frequently Asked Questions (FAQ) About Annuity and Perpetuity

  1. What is the difference between an ordinary annuity and annuity due?

    The main difference between an ordinary annuity and annuity due is the point of time when a payment occurred in a period.

    Usually, payments are granted at the end of the period in an ordinary annuity whereas, an annuity due, they are paid at the beginning of the period.

  2. How do you find the annuity factor?

    The annuity factor is generally used to find out the total present value of a fixed annuity. It is also used to calculate equated monthly installments.

    Annuity factor can be understood with the help of following formula:
    AF = (1-(1+r)^-n)/r

    Here AF is annuity factor, r stands for periodic rate and n stands for a number of consecutive withdrawals.

  3. What decreases the present value of an annuity?

    The present value of annuity gives a specified amount of rate or discounts. The present value of an annuity can be decreased by the higher discount rates that have an adverse effect on the present value of an annuity.

    The cash flow of an annuity is discounted by the discount rate hence result in a dropped value.

  4. What do you mean by perpetual annuity?

    A perpetual annuity is a form of an ordinary annuity. It is a security that continues forever which means this annuity has no end. The perpetual annuity pays a never-ending cash flow in finance.

    The present value of perpetuity can be calculated by the following formula:
    PV = C/(1+r)1 + C/(1+r)2 + C/(1+r)3

    Here PV stands for present value, C stands for cash flow and r stands for the discount rate. One such example of a perpetual annuity is the United Kingdom’s government bond which is known as Consol.

  5. Is pension the same as perpetuity?

    Pension is a type of retirement account where you keep saving throughout your entire life. On the other hand, perpetuity is an annuity that not only makes regular payments throughout the year but the payments never end as well.

    If you choose a defined benefit pension, you will get a regular income for life once you retire. But eventually, it ends once you die, hence it cannot be counted as perpetuity.

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Conclusion

Annuity and Perpetuity are similar in case of regular payments. But the two terms are very much different if studied deeply.

Where an Annuity’s payment is made or received for a particular time, a perpetuity’s payment is made forever.

The future value of an Annuity can be calculated using compound interest whereas it is not possible in case of Perpetuity.

Perpetuity is a less used concept compared to Annuity which is used often. In the calculation of the Present Value of an Annuity, compound interest is used.

On the other hand, we use simple interest in the calculation of the Present Value of a Perpetuity.

To find the Present Value of a Perpetuity we divide the cash flow (periodic payments) by interest rate. Perpetuity is somewhat a more theoretical concept and has less practical application.

An annuity is more practical as both future value and present value can easily be calculated by using the compound interest.

Both terminologies are studies under the topic –“Time Value of Money”. Understanding Annuity and Perpetuity gives a clear view to a person who wants to invest in retirement plans, life insurance or wants to invest in bonds based on Perpetuity.

Understanding these terms makes it easy for a person to make the right decisions with his or her money.

The financial market often uses such term, that’s why it becomes necessary to have perfect knowledge of such concepts.  


 

Word Cloud for Difference Between Annuity and Perpetuity

The following is a collection of the most used terms in this article on Annuity and Perpetuity. This should help in recalling related terms as used in this article at a later stage for you.

Annuity and Perpetuity
Word Cloud for Annuity and Perpetuity

 

References

  1. https://digitalcommons.georgefox.edu/cgi/viewcontent.cgi?article=1114&context=gfsb
  2. https://iabe.org/domains/iabeX/Documents/Proceedings/IABE-2009%20Las%20Vegas-%20Proceedings.pdf#page=105
  3. https://www.tandfonline.com/doi/abs/10.2469/faj.v56.n2.2345