Final answer:
The APY can be calculated using the formula APY = (1 + r/n)^(n*t) - 1, with an APR of 5.2% compounded daily resulting in a slightly higher yield than the nominal rate due to daily compounding.
Step-by-step explanation:
To find the annual percentage yield (APY) of a bank account with an annual percentage rate (APR) of 5.2%, compounded daily, we use the formula APY = (1 + r/n)^(n*t) - 1, where r is the decimal form of the APR, n is the number of compounding periods per year, and t is the time in years.
Here, the APR is 5.2% or 0.052 in decimal form, n is 365 (since compounding is daily), and t is 1 year. Plugging these into the formula, we get: APY = (1 + 0.052/365)^(365*1) - 1. After calculating the values within the parentheses and raising to the power of 365, we subtract 1 to find the APY.
The APY can be a more accurate reflection of the actual interest earned than the APR, especially when interest compounds more frequently than once a year. Daily compounding, as in this case, will yield a slightly higher APY than the nominal APR due to the effect of compound interest.