How to Calculate APR from EAR with Monthly Compounding

Question:

You have an outstanding loan with an EAR of 14.61 percent. What is the APR if interest is compounded monthly?

Answer:

The APR with monthly compounding for a loan with an EAR of 14.61% is approximately 13.68%.

When dealing with loans and interest rates, it's important to understand the difference between EAR (Effective Annual Rate) and APR (Annual Percentage Rate). The EAR represents the true annual interest rate, while the APR is the annual rate charged for borrowing.

To calculate the APR from the EAR with monthly compounding, you can use the formula:

APR = [ (1 + EAR)^(1/n) - 1 ] * n * 100%

For this specific case where the EAR is 14.61% and interest is compounded monthly (n = 12), you can plug in the values:

APR = [(1 + 0.1461)^(1/12) - 1] * 12 * 100%

By solving this equation, you will find that the APR is approximately 13.68%. This means that, when considering the compounding effect of interest on your loan, the annual percentage rate you are paying is around 13.68%.