Final answer:
The assumption that the compounding period matches the period of interest rate expression when not stated is false; both must be specified for accurate interest calculations. Compound interest and compound growth rates both cause exponential growth due to interest/growth on the accumulated amount.
Step-by-step explanation:
The statement that if the compounding period is not stated for a particular interest rate, it is assumed to be equal to the period over which the interest rate is expressed, is generally considered false. Lenders and financial institutions usually specify the compounding period, and if it is not specified, one cannot assume it matches the period of the interest rate expression. It is important to clarify the compounding period to accurately calculate the interest on a financial instrument.
Both compound growth rates and compound interest rates involve the principle of obtaining interest or growth on previously accumulated interest or growth, leading to exponential growth over time. The formula used to calculate the future value with compound interest is:
Future Value = Principal x (1 + interest rate)time
Compound interest = Future Value - Present Value
Similarly, the compound growth rate for something like GDP considers growth over the previous period, leading to potentially dramatic increases over time, just as with compound interest when applied to financial savings.