Annuity factor

From ACT Wiki
Revision as of 10:43, 11 June 2013 by imported>Doug Williamson (Formatting, punctuation and adding examples to line up with improved Discount Factor page.)
Jump to navigationJump to search

Financial maths.

(AF).

A method for calculating the total present value of a simple fixed annuity.

Mathematically, the Annuity Factor is the cumulative Discount Factor for maturities 1 to n inclusive, when the periodic cost of capital is the same for all relevant maturities.


Commonly abbreviated as AF(n,r) or AFn


Present value calculation

The present value of the annuity is calculated from the Annuity Factor (AF) as:

= AF x Time 1 cash flow.


Example

For example, when the Annuity factor = 1.833 and the Time 1 cash flow = $10, then:

Present value = AF x Time 1 cash flow

= 1.833 x $10

= $18.33


Annuity factor calculation

The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as:

AF(n,r) = 1/r x [1-(1+r)-n]


where

n = number of periods, and

r = periodic cost of capital.


Example

For example, when the periodic cost of capital (r) = 6% and the number of periods in the total time under review (n) = 2, then:

Annuity factor = 1/r x [1-(1+r)-n]

= 1/0.06 x [1-(1 + 0.06)-2]

= 1.833


This figure is also the sum of the two related Discount Factors:

AF2 = DF1 + DF2

= 1.06-1 + 1.06-2

= 0.9434 + 0.8900

= 1.833


The Annuity Factor is sometimes also known as the Annuity formula.

See also