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:

Formula

Let:

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

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

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

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

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

Then:

A = W P V I F {\displaystyle A={\frac {W}{PVIF}}}

where

P V I F = 1 m ⋅ 1 − ( 1 + i ) − n ( 1 + i ) 1 / m − 1 {\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:

P V I F = ( 1 + r ) − n {\displaystyle PVIF=(1+r)^{-n}}

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

See also