Time value of money concerns equivalence relationships between cash flows occurring on different dates. The idea of equivalence relationships is relatively simple.
Consider the following exchange: You pay \$10,000 today and in return receive \$9,500 today. Would you accept this arrangement? Not likely. But what if you received the \$ 9,500 today and paid the \$ 10,000 one year from now? Can these amounts be considered equivalent?
Possibly, because a payment of \$ 10,000 a year from now would probably be worth less to you than a payment of \$ 10,000 today. It would be fair, therefore, to discount the \$ 10,000 received in one year; that is, to cut its value based on how much time passes before the money is paid.
An interest rate. denoted $r$, is a rate of return that reflects the relationship between differently dated cash flows. If \$ 9,500 today and \$ 10,000 in one year are equivalent in value, then \$ 10,000 - \$ 9,500 =\$ 500 is the required compensation for receiving \$ 10,000 in one year rather than now.
The interest rate - the required compensation stated as a rate of return - is \$ 500 / \$ 9,500=0.0526 or 5.26 percent.