Present value interest factor

In economics, present value interest factor (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:

$W$ = the amount borrowed (loan)

$i$ = the effective (i.e. convertible annually) annual interest rate charged

$n$ = the number of years over which the loan will be outstanding

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

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

Then:

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

where

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

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

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

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

See also

• Time value of money
• Life annuity
• Fixed-rate mortgage
• Amortization calculator