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

Jul 4, 2015

The amount a future sum of money is worth at some period before that.

#### Explanation:

Let's being with a basic rule: an amount of money will be worth different values at different points in time, assuming money has a cost - an interest rate, or rate of return.

Here is a simple example that will help organize our thinking. Let's assume you want to have $10,000 in 5 years so you can celebrate your graduation by trekking the Camino de Santiago. How much will you need to invest today to reach your target? We know the future value is$10,000. And the present value is unknown.

It is easy to calculate the present value using this formula

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

We will assume the rate of return (r) that we can earn on our invested money is 6%. And we need the money in 5 years (n), so

$P V = \frac{10 , 000}{1.06} ^ 5$

$P V = \frac{10 , 000}{1.3382}$

PV = $7,472.58 The answer tells us that the present value of$10,000 in 5 years is $7,472.58 today, if we can invest money at 6%. Your$7,472.58 will grow to \$10,000 in 5 years, if it is invested at 6% annually.