# Annuity vs Perpetuity

Published on :

21 Aug, 2024

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Edited by :

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Reviewed by :

Dheeraj Vaidya

## Difference Between Annuity and Perpetuity

Annuity refers to regular payments for a certain period of time under some contract or agreement with an insurance company and present value of annuity is determined by taking the present value of future payments by discounting it at compounding rate whereas perpetuity refers to the infinite payments at fixed rate forever and it is calculated using simple interest formula.

Both are implicated while calculating the present or future value of a financial product and are significant parts of the Time Value of Money calculation.

• Annuity means when a series of the same amount of cash flow is received or paid over the life of the asset on a monthly, quarterly, semi-annually, or annually basis.
• Whereas Perpetuity means when a series of the same amount of cash flow received or paid forever on a specified time-frequency. Hence, we can say that infinity is similar to Annuity, which will last till infinity.

These financial management concepts are used in our routine life, like purchasing a car on bank finance and repaying the loan in sequential EMIs’ or paying regular lease amounts to our landlord. Here we will understand both the concept of the time value of money in detail.

### Key Differences

• An annuity is a finite stream of cash flows received or paid at specified intervals, whereas Perpetuity is a sort of ordinary Annuity that will last forever, into Perpetuity.
• An annuity can further be defined in two types, i.e., Ordinary Annuity and Annuity Due. An Ordinary Annuity means payments are required to be made at the end of each period, e.g., Plain Vanilla Bonds make their coupon payments at the end of each period until the life of the Bond. Whereas in Annuity Due, fees are required to be paid at the beginning of the period, e.g., Rent paid in advance for every month until the let out period.
• Due to its tough time, Perpetuity is not utilized for many financial assets other than Annuity.
• There are no further types of Perpetuity and consols, i.e., Bonds issued by the UK Government, which will make the coupon payments till the infinity or stocks paying a constant dividend are the best examples of Perpetuity.
• As an annuity has a specified time, it uses the compound interest rate to calculate the future value of a stream of cash flow. It means, while deriving the value of an Annuity, it’s required to compound cash flow and interest rate, which is earned every year, till the life of Annuity. Whereas Perpetuity has infinite time, it uses a simple interest rate or stated interest rate only. The Perpetuity owner will receive a constant amount of cash flow forever.
• One can calculate the present value of Annuity by discounting annuity cash flows and future value of Annuity by compounding annuity cash flows at the specified interest rate. While the future value of Perpetuity is indeterminable due to its perpetual nature of cash flow, its PV in excel can be calculated and which is equal to the sum of the discounted value of each periodic cash flow.
• The formula for calculating the present value of Annuity Due, Ordinary Annuity and Perpetuity are as below –
• Present Value of Ordinary Annuity = A *
• Present Value of Annuity Due = A * * (1 + r)
• Present Value of Perpetuity = A / r
• Where, A = Annuity Amount, r = Interest Rate per Period and n = Number of Payment Periods

### Conclusion

We can conclude that Perpetuity is a perpetual annuity. The only difference between them is their time. On the one hand, an annuity has a finite set of sequential cash flows. On the other hand, Perpetuity doesn’t have any specified existence, and its payment frequency extends indefinitely.

While calculating the present value or future value of Annuity, you must have to consider cash flow, cash flow frequencies, interest rate, and the time at which the first payment is made, i.e., at the beginning of the period or the end of the period. But the calculation of Perpetuity is quite simple, and while calculating the present value of the Perpetuity, you only need to consider the cash flow and the stated interest rate.

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