Final answer:
The annual percentage yield (APY) can be found using the formula (1 + r/n)^n - 1, where r is the annual interest rate and n is the number of times interest is compounded per year. The APY is greater than the APR because it takes compounding into account. If the bank compounded continuously, the APY would be slightly higher.
Step-by-step explanation:
The annual percentage yield (APY) can be found by using the formula: APY = (1 + r/n)^n - 1 Where r is the annual interest rate and n is the number of times interest is compounded per year. In this case, the APR is 4.5% and interest is compounded quarterly, so n = 4. Substituting these values, we get: APY = (1 + 0.045/4)^4 - 1, APY ≈ 0.0463559 The APY is greater than the APR because it takes compounding into account. When interest is compounded, the interest earned on previous interest is added to the principal, resulting in a higher overall yield.
The APY is greater than the APR because it takes compounding into account. When interest is compounded, the interest earned on previous interest is added to the principal, resulting in a higher overall yield. If the bank compounded continuously, the APY would be affected by the continuous compounding formula: APY = e^r - 1, Where e is Euler's number (approximately 2.71828) and r is the annual interest rate. Substituting the values, we get: APY = e^(0.045) - 1 ≈ 0.046899, The APY would be slightly higher with continuous compounding compared to quarterly compounding.