A bank advertises an APR of 5.5% on personal loans. How much more is the APY when the rate is compounded monthly as compared to when it’s compounded quarterly? explain your answer.
The Annual Percentage Rate (APR) is the annualized interest rate that does not take into account the effects of compounding. On the other hand, the Annual Percentage Yield (APY) does take compounding into account and reflects the actual annual interest earned on an investment or loan.
When the APR is compounded monthly, the effective interest rate will be slightly higher than when it is compounded quarterly. This is because with monthly compounding, interest is added to the principal more frequently throughout the year, allowing the balance to grow faster.
To calculate the APY when the APR is compounded monthly:
APY = (1 + APR/n)^n - 1, where n is the number of compounding periods per year
With an APR of 5.5% and monthly compounding (n = 12), the APY would be:
APY = (1 + 0.055/12)^12 - 1
APY = (1.0045833)^12 - 1
APY ≈ 5.68%
To calculate the APY when the APR is compounded quarterly:
APY = (1 + APR/4)^4 - 1
With an APR of 5.5% and quarterly compounding (n = 4), the APY would be:
APY = (1 + 0.055/4)^4 - 1
APY = (1.01375)^4 - 1
APY ≈ 5.61%
Therefore, the difference in APY between monthly compounding and quarterly compounding is approximately 0.07%. This means that the APY is slightly higher when the APR is compounded monthly compared to quarterly.