# What is the future value of a sum of money?

Dec 17, 2014

The future value of a sum of money is given by 'growing' the current value of that money at the appropriate interest rate (or return rate) over the relevant period of time.

A simple formula is:

$F V = P V {\left(1 + r\right)}^{n}$

What this says is that the future value (FV) is equal to the present value (PV) grown at the rate 'r' over 'n' periods.

An example may make it easier. Consider you have $100 today that you invest at 10% per annum compounded annually. What is the future value of this$100 after 1 year? What about after 3 years?

a) After one year: $F V = 100 {\left(1 + 0.1\right)}^{1} = 110$
b) After three years: $F V = 100 {\left(1 + 0.1\right)}^{3} = 133.$

Note that the present value of a sum of money can be calculated with just a slight manipulation of the same formula:

$P V = \frac{F V}{1 + r} ^ n$