Final answer:
Loan A has an annual percentage yield (APY) of approximately 10.7%, while Loan B has an APY of approximately 9.8%, when both are rounded to one decimal place. Loan A offers a higher APY due to its higher nominal interest rate and more frequent compounding intervals.
Step-by-step explanation:
To compare the annual percentage yield (APY) of two loans with different compounding intervals, we can use the formula for APY, which is APY = (1 + r/n)n - 1, where r is the nominal interest rate and n is the number of compounding periods per year.
For loan A, with a nominal interest rate of 10.2% (or 0.102) and daily compounding, n would be 365 because there are 365 days in a year. Therefore, the APY for loan A can be calculated as:
APY for Loan A = (1 + 0.102/365)365 - 1 ≈ 0.1071 or 10.7% when rounded to one decimal place.
For loan B, with a nominal interest rate of 9.6% (or 0.096) and quarterly compounding, n would be 4 because there are 4 quarters in a year. Consequently, the APY for loan B is:
APY for Loan B = (1 + 0.096/4)4 - 1 ≈ 0.0984 or 9.8% when rounded to one decimal place.
Comparing the two APYs, loan A with a higher nominal interest rate and more frequent compounding intervals offers a higher APY than loan B.