Present value interest factor

In economics, Present value interest factor, also known by the acronym PVIF, is used in finance theory to refer to the output of a calculation, used to determine the monthly payment needed to repay a loan. The calculation involves a number of variables, which are set out in the following description of the calculation:

Let:

${\displaystyle W}$ = the amount borrowed (loan)

${\displaystyle i}$ = the effective (i.e. convertible annually) annual interest rate charged

${\displaystyle n}$ = the number of years over which the loan will be outstanding

${\displaystyle A}$ = the annual amount of the fixed regular payments that will amortize (i.e. repay) the loan

${\displaystyle m}$ = the frequency of these regular payments, e.g. m = 2 means the payments are half-yearly.

Then:

${\displaystyle A={\frac {W}{PVIF}}}$

where

${\displaystyle PVIF={\frac {1}{m}}\cdot {\frac {1-(1+i)^{-n}}{(1+i)^{1/m}-1}}}$

In its simplest form,  PVIF  is calculated using the formula:

${\displaystyle PVIF=(1+r)^{-n}}$

where ${\displaystyle r}$ is the discount rate (or interest rate) and ${\displaystyle n}$ is the number of periods.