Time value of money#Present value of an annuity for n payment periods

The annuity value is the initial capital required to pay at a given interest rate future cash benefit ( pension) in a specific amount at a specific point in time. He also discusses the value of a pension corresponding to the time of observation. The annuity value factor (RBF ) (also Diskontierungssummenfaktor ) or Annuitätenbarwertfaktor ( ABWF ) is part of the annuity of the classical dynamic investment calculation. The mathematical formula makes it possible to calculate the present value of a uniform series of payments ( annuity payment ). If an investment generates a constant annual payment ( a so-called annuity), it can be easily calculated the net present value of all payments by the annuity is multiplied by the annuity value factor.

The annuity value factor for an annuity pension is calculated by

In which

  • Number of Periods
  • Interest rate for each such period.

If it is stated in years, the annual interest rate (eg 4.5% interest rate is 0.045 ).

If the zero rate of interest shall be deemed

Otherwise

The annuity factor (ANF, recovery factor) is the reciprocal ( inverse ) of the annuity value factor:

Examples

The annuity value factor at a positive interest rate i

  • No payments for zero
  • For a single payment in arrears 1 / ( 1 i) ( 1 / ( 1 i) is less than 1 and greater than 1, i)
  • For an annuity in perpetuity 1 / i, for advance payments perpetuity (1 i) / i

At an interest rate of 0, the annuity value factor is the number of periods.

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