Final answer:
The statement about effective annual interest rate (EAR) being the annual growth rate accounting for compounding is true. EAR is used to truly understand the growth of investments with compounding, much like how compounded rates impact economic growth and productivity.
Step-by-step explanation:
The statement that the effective annual interest rate (EAR) is the annual growth rate that takes compounding into account is true. The EAR is crucial in comparing different financial products that might have various compounding periods. This calculation allows individuals to understand the actual rate at which their investment will grow within a year considering the effects of compound interest. Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods.
Understanding EAR is essential, as compound interest and rates, similar to those of economic growth or productivity rates, highlight that even minute changes in rates can lead to significant differences in growth over time. For instance, an economic growth rate of 8% can result in a staggering increase in the GDP or the standard of living within a relatively short period. The compound growth rate involves multiplying the rate of growth by a base including past growth, which amplifies the impact dramatically over time. The formula used for calculating GDP growth rates and compound interest on savings is essentially the same, including an original amount, a percentage increase, and the time of growth.