Final answer:
Discounting and compounding are inverse processes related to the value of money over time. Compounding increases the future value as it calculates interest on interest, while discounting finds the present value by considering the time value of money.
Step-by-step explanation:
The relationship between discounting and compounding relates to the way value changes over time. Discounting is the reverse process of compounding; while compounding involves calculating the future value of money based on the principal and accumulated interest over time, discounting determines the present value of future cash flows by removing the time value of money.
When we compound, we apply an interest rate to the principal amount plus any accumulated interest from previous periods, leading to an increase in the future value of money.
This concept is not only applicable to personal financial savings but also mirrors the way gross domestic product (GDP) growth rates are calculated in economics, where the GDP grows by a certain percentage over time. Similar to how compound interest is interest on interest, compound growth rates mean we multiply the rate of economic growth by the base that includes past GDP growth, resulting in significant changes over time.
The calculation for future value using the compounding method is:
Future Value = Principal x (1 + interest rate)^time
Compound interest, therefore, is the difference between the future value and the present value. Discounting, on the other hand, is often applied to various cash flows, not only to interest rates, to obtain the present value.