Final answer:
The Annual Percentage Yield (APY) for an account with a 4.5% annual percentage rate (APR), compounded daily, can be calculated using the APY formula, resulting in an APY of approximately 4.56%.
Step-by-step explanation:
To calculate the annual percentage yield (APY) for an account with an annual percentage rate (APR) of 4.5%, compounded daily, we use the formula for APY, which includes the effect of compounding:
APY = (1 + r/n)^(n∗t) - 1
where:
r is the annual interest rate (decimal),
n is the number of times the interest is compounded per year,
and t is the time in years.
For daily compounding, n would be 365. As we're looking for the yield over one year, t will be 1. Converting the APR from a percentage to a decimal, we get r = 0.045. Substituting into the formula, we get:
APY = (1 + 0.045/365)^(365∗t) - 1
APY = (1 + 0.00012328767123)^(365) - 1
APY = 1.0456436200818 - 1
APY = 0.0456436200818
Converting this back into a percentage, we multiply by 100:
APY = 4.56436200818%
Thus, the Annual Percentage Yield for an account with a 4.5% APR compounded daily is approximately 4.56%.