Perpetuity

A perpetual annuity (also Perpetuität ) is a pension that can be paid from the interest income of a fixed-income investment, without changing the value of the invested capital. As an example, the Nobel Prize is named, which is paid annually to outstanding scientists. This prize is worth around 1 million euros (depending on the interest income ) per subject.

As the capital will be preserved, the yield (r ) is therefore achieved "forever".

Calculation

R is the repeated (retrospectively ) to be paid pension amount, the initial capital K and p is the discount rate.

Derivation

The formula of the reversionary annuity present value comes from the pension bill.

Example of use

The method of " perpetuity " is suitable for decision-making " Rent or Sell ". For example, from the seller's perspective, the selling price K of a property including selling costs, is less than the quotient of the expected annual net rental income ( rental income minus maintenance costs, taxes, etc.) and the rate that rental is advantageous.

Eternal rising and falling pensions

Of course, there is the concept of rising and falling bond even in the perpetuity. Question is based on the consideration of the guaranteed value of the periodic payments of interest ( inflation). Thus it can be taken from an eternal rising pension annually increased by the slope factor amount without touching the capital and to prevent annual increases. In this case, the formula

R again denotes the periodic annuity annuity payment, the initial capital K, p the interest rate and g is the periodic growth rate ( growth rate ).

It must be noted that the growth rate may also have a negative sign. The " pitch " is then negative, and it is in this case a falling pension.

Application example for an eternal, rising pension

A typical example can be found in the final disposal of radioactive waste. Annual running here at a cost that must be paid to all eternity. However, the inflation rate must be considered. So you define a realistic growth rate (eg 3 %) and can now calculate the necessary capital stock, which one needed to pay all lying in the future, with the inflation rate every year - in the formula represented by g - to increase, may cover.