## 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.

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Source: Annuity vs Perpetuity (wallstreetmojo.com)

- 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 leaseLeaseLeasing is an arrangement in which the asset's right is transferred to another person without transferring the ownership. In simple terms, it means giving the asset on hire or rent. The person who gives the asset is “Lessor,” the person who takes the asset on rent is “Lessee.”read more amounts to our landlord. Here we will understand both the concept of the time value of money in detail.

### Annuity vs. Perpetuity Infographics

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### 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 assetsMany Financial AssetsFinancial assets are investment assets whose value derives from a contractual claim on what they represent. These are liquid assets because the economic resources or ownership can be converted into a valuable asset such as cash.read more 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 AnnuityFuture Value Of AnnuityThe future value of annuity due is the amount to be received in future where each payment is made at the beginning of each period. FVA due = P * [(1 + r)n – 1] * (1 + r)/rread more 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 excelPV In ExcelPV, or present value, is a function that is used to calculate the current present value of any investment. It is determined by the investment rate and the number of payment periods, with the future value as an input.read more 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 AnnuityCalculating The Present Value Of AnnuityThe present value of an annuity formula depicts the current value of the future annuity payments. Present Value of an Annuity=C×(1−〖(1+i)〗^(−n))/i, where C is the cash flow per period, i is the interest rate, and n is the frequency of payments.read more Due, Ordinary Annuity and Perpetuity are as below –
**Present Value of Ordinary Annuity = A * [{1 – (1 + r)**^{-n}} / r ]**Present Value of Annuity Due = A * [{1 – (1 + r)**^{-n}} / r ] * (1 + r)**Present Value of Perpetuity = A / r**- Where,
**A**= Annuity Amount,**r**= Interest Rate per Period and**n**= Number of Payment Periods

### Perpetuity vs. Annuity – Comparative Table

### 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 it’s 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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