## Interest Rate Conversion: Meet the NPEPN

Hello and welcome. In this video, I’ll show you how to convert interest rates using a very handy shortcut called the NPEPN. Let’s dive right in. Let’s say you are looking to get a loan to buy a boat and you see that 2 different banks offer different rates. One bank offers j2 = 12% and the other one offers j12 = 11.75%. Hmm now the second rate looks lower but it has different number of compounding periods. And now you know that compounding can make a difference. So which rate should you, the borrower, choose? Well, we can’t compare these rates directly because they have different compounding periods. It would be like comparing apples and oranges. So we have to convert them to have the same number of compounding periods. This way we will be comparing apples to apples and we will see which one is lower. The most straightforward option is to convert them both to j1. Let’s do this using the financial calculator. Let’s convert j2 = 12% to j1. We will do that using a very handy shortcut. It’s called the NPEPN. The NPEPN is just a way to remember this order of keys: Nom (stands for nominal) P/YR (stands for compounding periods per year) Eff (stands for effective) then P/YR and Nom again. Note that all these keys are orange on your calculator, so you will need to use the orange SHIFT key for each one of them The way NPEPN works is you put the rate your know at the top and at the bottom you put what compounding periods you want to convert to. So in our case we have j2 = 12% so I put 12 for the top Nom and 2 for the top P/YR I want to convert this rate to j1 (I want to have 1 compounding period I WANNA HAVE EFFECTIVE RATE), so I put 1 for the bottom P/YR. That’s all I need to do the conversion. Now I simply start going through the NPEPN. Type 12 and press SHIFT Nom, type 2 and press SHIFT P/YR press SHIFT EFF, TYPE 1 and press SHIFT P/YR Now press SHIFT Nom and WHAT you see on the screen is the equivalent j1. So the j1 that’s equivalent to our j12 is 12.36%. We have converted our rate to J1. This means that effectively (that’s why this rate is called effective), 12..36% will be added to the loan amount at the end of the year. Now let’s convert the other rate to j1 as well and see if it comes out higher or lower. Let’s covert j12 = 11.75% to j1. Again, I put what I know at the top Nom is 11.75 and P/YR is 12 I want to have j1 so I want my P/YR as 1. I put that at the bottom Type 11.75 and press SHIFT Nom, type 12 and press SHIFT P/YR press SHIFT EFF, TYPE 1 and press SHIFT P/YR Now press SHIFT Nom and what you see on the screen is the equivalent j1. So the j1 that’s equivalent to our j12 is 12.403902% Ok so we converted our rates to j1. And we can now see that the one on the left is the lower rate. So as a borrower, you’d choose to borrow at j2 = 12%. Now we can see THAT it is the lower rate so you’ll simply owe less money to the bank at the end of the loan. But if you are an investor then OF COURSE you would prefer to invest at a higher rate, so the option on the right is what you would choose. You have seen how to use the NPEPN to convert to j1. Let’s do one more example where we convert to something else. Let’s convert j2 = 5% to j12. This is a conversion you will see a lot in this course because mortgage rates are given by banks as j2 but the mortgage payments are monthly so the rate ALWAYS needs to be converted to monthly compounding. You will see lots of examples of this later in the course. To convert j2 = 5% to j12 we use the NPEPN in the same way we did before. We put what we have at the top (Nom is 5 and P/YR is 2), And we put what we want at the bottom (We want to have j12 so we want our P/YR to be 12). Now you type 5 press shift NOM, 2 SHIFT P/YR. Now press SHIFT EFF. I’d like to pause here for a moment. When you are doing the NPEPN and you press SHIFT EFF what you see on the screen is the equivalent j1. So if you were converting to j1 you can actually stop right here to save time, you don’t need to enter 1 for P/YR and press SHIFT NOM. You can and you’d get the same answer, but if you are converting to j1 you are better off just stopping here to save time. So in the first two examples when we were converting to j1 we actually could have stopped here. If you want you can go back and check – you will see that we get the right answer already at this step. But in this example we are NOT converting to effective, we are converting to j12, so we will continue with the full NPEPN Type 12 and press SHIFT P/YR Press SHIFT Nom The rate you see on the screen is the j12 that’s equivalent to j2=5%. NOW YOU KNOW HOW TO CONVERT INTEREST RATES TO EFFECTIVE AND TO A DIFFERENT COMPOUNIDNG FREQUENCY