Time Value of Money

In economics, present value, also known as present discounted value, is a future amount of money that has been discounted to reflect its current value, as if it existed today. The present value is always less than or equal to the future value because money has interest-earning potential, a characteristic referred to as the time value of money.

Expressed mathematically, present value = pv and future value = fv

fv = pv(1+ iT)

i is the annual interest rate and T is the time period between the present and future.

It follows that (1)  pv = fv (1 – iT)

Define the ratio pv/fv as u and dividing (1) by fv gives

(2)  u = 1-iT     If the period of interest is one year,  then T = 1/V, where V is the velocity of money which is the rate of circulation of money per time unit so that

u = 1 – i/V

Thus (3)  i = V(1-u)  is an expression for the interest rate in terms of money velocity and debt.

u is the cash value of  income Y=1.  1-u is the debt portion of income on a future value basis.

http://www.fiscal.treasury.gov/fsreports/rpt/goldRpt/current_report.htm