Annuity factor

Financial maths.

(AF).

1.

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 cost of capital is the same for all relevant maturities.

Commonly abbreviated as AF(n,r) or AF_n

Also known as the Present Value Interest Factor of an Annuity (PVIFA).

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 = $10m, then:

Present value = AF x Time 1 cash flow

= 1.833 x $10m

= $18.33m

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

2.

Annuity factors are also used to calculate equated loan instalments.

For a loan drawn down in full at the start, the equated loan instalment is given by:

Instalment = Principal/Annuity factor

Example

$20m is borrowed at an annual interest rate of 6%.

The loan is to be repaid in two equal annual instalments, starting one year from now.

The annuity factor is 1.833 (as before).

The loan instalment is:

$20m/1.833

= $10.9m

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

See also

• Annuity
• Annuity formula
• CertFMM
• Discount factor
• Perpetuity factor
• Present value
• Instalment
• Equated instalment
• Principal