How do compounding and discounting primarily differ in financial calculations?

Compounding and discounting are two fundamental concepts in finance that are used to calculate the value of money over time, but they are applied in opposite directions.

Compounding is the process of determining the future value of a sum of money based on its current value and an interest rate over a specified period. Essentially, compounding takes into account not only the interest earned on the initial principal but also the interest that has been added to it over time. This means that the longer the money is invested or borrowed, the more interest accumulates, leading to exponential growth.

On the other hand, discounting is the reverse process. It calculates the present value of a future amount of money, considering a specific discount rate. This is critical for understanding what a future cash flow is worth today, given the opportunity cost of capital. Discounting allows investors or borrowers to evaluate the worth of future cash flows in today's terms, taking into account the time value of money.

Thus, the distinction lies in their purposes: while compounding is used to estimate how much an investment will grow in the future (future value), discounting is utilized to find out how much future cash flows are valued in today’s money (present value).