Week 7 Converting Compounding Rates to the EAR

Week 7: Lecture

Converting Daily/Weekly/Monthly Compounding Rates To The EAR

As we said earlier, most of the time in finance we deal with things on an annual basis, and in nearly all cases interest rates are quoted on an annual basis. For this reason it is important to be able to adjust the interest rate from daily, weekly, or monthly compounding to an Equivalent Annual Rate (EAR), as if the interest were being compounded annually. The procedure for doing this is as follows:

Where: "m" = the number of compounding periods in a year i.e.,

365 for daily
52 for weekly
12 for monthly
4 for quarterly (and so on)

Example: Your bank advertises loan rates of 12%, compounded monthly. What is the EAR?

Note: Sometimes you are given the interest rate per period (monthly daily, etc.) directly. In these situations you don’t need to divide the rate by the number of compounding periods in a year to annualize it. You simply plug the rate per period into the EAR equation like this:

Example: Your credit card statement says you are charged 1% a month on unpaid balances. What is the EAR?