A perpetual annuity is a constant and unlimited flow of payments. An example of such a perpetual annuity is a pension from an endowment fund.

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## Definition / explanation

If the originally available capital is not used in a payment and there is no time limit for the payment, one speaks of a perpetual annuity.

The perpetual annuity is calculated by multiplying the initial capital and the discount rate:

r = K xp

r = the repeatedly (in arrears) to be paid pension amount

K = initial capital

p = discount rate

## Areas of application of the perpetual annuity

Ein Anwendungsgebiet der ewigen Rente ist die Company valuation. Unternehmen haben in der Regel keine Laufzeit, sondern werden als ewig vorhanden angesehen.

Another area of application is the decision-making process whether a property should be rented or sold. Here it must first be calculated how high the sales value K including the incidental costs is. In the second step, the quotient is calculated from the annual net rent and the calculated interest rate. If the sales price is lower than the annual net rental income, it makes more sense for the owner to rent out the property.

## Eternal rising and falling pensions

The perpetual annuity method can also be applied to slightly changing values.

**Example:** In the long term, radioactive waste has to be stored forever and thus paid for. In order to be able to settle these annual costs and to make the necessary capital plannable, the inflation rate must be factored into the amount of the payments. The formula for this is:

r = K x (p - g)

r = the repeatedly (in arrears) to be paid pension amount

K = initial capital

p = discount rate

g = periodic growth rate

## Summary

- Perpetual annuities are constant payments without reducing the previously existing capital
- perpetual annuity is calculated by multiplying the initial capital and the discount rate
- Areas of use are company valuation and the question of sales or letting in the real estate industry
- Calculation also possible for rising and falling perpetual annuities