# 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**. http://en.wikipedia.org/wiki/Present_value

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

fv = pv+ iT

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

It follows that **(1)** pv = fv – iT

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

**(2)** u = 1 – iT/fv or **(2a)** iT/fv = 1 – u

If the period of interest is one year, then T = 1/V, where V is the annual **velocity of money** which is the rate of circulation of money per year. And further if fv = 1 , e.g. = $1, then the present value of that amount which has a future value after 1 year is

u = 1 – i/V so that **(3)** i = V(1-u) defines the interest rate in terms of velocity and present value. Both V and u vary continuously over the loan period, while future value fv = 1 is constant.

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