What relationship do compounding and discounting have?

Compounding and discounting are fundamentally related concepts in finance, and they can be viewed as opposites in the context of time value of money. Compounding involves calculating the future value of an investment based on an initial principal amount and adding interest over time, whereas discounting is the process of determining the present value of a future cash flow by accounting for the time value of money. In essence, compounding moves money forward in time to its future value, while discounting brings a future amount back to its present value.

This relationship highlights the fundamental principle of time value of money: a dollar today is worth more than a dollar tomorrow due to its potential earning capacity. The two processes rely on the same interest rate but operate in reverse directions - compounding increasing the amount over time and discounting decreasing the future amount back to present value. Understanding this relationship is crucial for making informed financial decisions, such as evaluating investments or loan repayments.