Final answer:
The Annual Percentage Yield (APY) for an 11% rate compounded quarterly and a 13% rate compounded continuously can be computed using specific mathematical formulas that account for the compounding frequency. The APY helps savers understand the actual return on their investment over time.
Step-by-step explanation:
To calculate the Annual Percentage Yield (APY) for money invested at different rates and compound frequencies, we can use specific formulae. For a rate that is compounded quarterly, such as an 11% annual interest rate, the formula is APY = (1 + r/n)^(n*t) - 1, where r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
For 11% compounded quarterly, the calculation would be APY = (1 + 0.11/4)^(4*1) - 1. We plug in the values to get an APY for case (A).
In the case of continuous compounding, such as a 13% annually compounded continuously, we use the formula APY = e^r - 1, where e is the base of the natural logarithm, approximately 2.71828, and r is the annual interest rate as a decimal. For 13% compounded continuously, the APY would be APY = e^0.13 - 1.