Annuity factor: Difference between revisions
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''Financial maths''. | ''Financial maths''. | ||
The present value of the annuity is | (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'' AF<SUB>n</SUB> | |||
== Present value calculation == | |||
The present value of the annuity is calculated from the Annuity Factor (AF) as: | |||
= AF x Time 1 cash flow. | = 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: | The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as: | ||
AF(n,r) = 1/r x [1-(1+r)<sup>-n</sup>] | AF(n,r) = 1/r x [1-(1+r)<sup>-n</sup>] | ||
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)<sup>-n</sup>] | |||
= 1/0.06 x [1-(1 + 0.06)<sup>-2</sup>] | |||
= '''1.833''' | |||
This figure is also the sum of the two related Discount Factors: | |||
AF<sub>2</sub> = DF<sub>1</sub> + DF<sub>2</sub> | |||
= 1.06<sup>-1</sup> + 1.06<sup>-2</sup> | |||
= 0.9434 + 0.8900 | |||
= 1.833 | |||
The Annuity Factor is sometimes also known as the Annuity formula. | |||
== See also == | == See also == | ||
Revision as of 10:43, 11 June 2013
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.
