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.
To calculate the APY for a loan that is compounded monthly, we use the formula:
APY = (1 + (r/n))^n - 1
where r is the annual interest rate and n is the number of compounding periods per year. In this case, r = 5.5% or 0.055 and n = 12 (since the loan is compounded monthly).
Using this formula, the APY for a loan with an APR of 5.5% compounded monthly is:
APY_monthly = (1 + (0.055/12))^12 - 1 ≈ 5.65%
To calculate the APY for a loan that is compounded quarterly, we use the same formula but with n = 4:
APY_quarterly = (1 + (0.055/4))^4 - 1 ≈ 5.57%
Therefore, the difference in APY between the monthly and quarterly compounding options is:
APY_monthly - APY_quarterly = 5.65% - 5.57% = 0.08%
Therefore, the APY is 0.08% higher when the loan is compounded monthly compared to quarterly. This difference may seem small, but over the course of a loan, it can add up to a significant amount of money saved or owed.