### Intro to Finance

## Time Value of Money

## What is the Time Value of Money?

One of the most fundamental concepts of finance is the time value of money, which essentially means that money now is more valuable than the same sum of money in the future. In other words, $100 today is worth more than $100 in 1 year. The principle behind this concept is the potential earning capacity of money. That is, you can invest the money you have today and make it grow over a period of time. There is an opportunity cost associated with waiting, such as the potential gain on interest were that money received today held in a savings account. That opportunity cost accounts for the difference between the value of money today and the value of money in the future.

## Present Value & Future Value

Since money today is worth more than money in the future, you must always discount money in the future to its value today, also called its Present Value. For example, let's assume that you will receive $1,000 in 1 year. In other words, the Future Value of the money that you will receive in 1 year is $1,000. What is the Present Value of that amount of money – i.e. what is that same amount of money worth today? The answer depends on your opportunity cost. If you can earn a 5% annual interest rate, then $1,000 in 1 year would be worth $1,000 / ((1+5%)^1), or $952.38 today. An easy way to understand this idea is that if you invested $952.38 today and received a 5% annual return, you would end up with exactly $1,000 in 1 year.

## Time Value of Money Formula

The most fundamental Time Value of Money formula takes into account the following variables:

PV: Present Value (what your money is worth right now)

FV: Future Value (what your money will be worth in the future if it earns interest)

r: (Annual) Interest Rate

t: Number of Years

Based on these variables, the formula is:

PV = FV / ((1+r)^t)

The formula can also be rearranged to find the Future Value of money today:

FV = PV x ((1+r)^t)

Test your understanding of the Time Value of Money: