Accrued Interest Mini-Lesson

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I want to talk about a concept called Accrued Interest when purchasing a bond. The reason why I want to cover this concept is that it is a little bit counter-intuitive to what a new student might think. After all, when you are buying a bond, you are buying it in the hopes of receiving interest income, right? So the concept of Accrued Interest can be a little counter-intuitive. You will see what I mean. If we take a look at this question together, in the video, that I’ve drafted for the purposes of this video. In this question, Jackie is about to retire and she requires regular income and as a result she decided to buy a bond with a 5% coupon rate and $100,000 face value in the secondary market from Fred.

You are being asked “Upon the sale of the bond, what is true of accrued interest?”. When you look at the answers the nuts and bolts of it is “Who pays the Accrued Interest to who?”. Does Fred pay it to Jackie, does Jackie pay it to Fred, does the issuer pay it to Jackie or to Fred? “What is the case here?”. The actual answer may give you, and then we’ll talk through it a little bit, because like I said, it’s a little counter-intuitive. The actual answer is ‘B’ – “The Accrued Interest is paid by Jackie who is buying the bond to Fred who is selling the bond”. As you can imagine, that might confuse Jackie, she might say, “Well, what do you mean here? I am buying a bond so that I can earn interest and then the very next thing I’m hearing is I have to pay accrued interest?”.

That doesn’t make a lot of sense, initially. Let’s talk through it because it does make a lot of sense once you understand it. First of all, you want to know this for the exam. Unless a scenario says otherwise you want to assume that a bond pays interest semi-annually, which is every six months. Let’s make a couple of assumptions so we can talk through this concept a little bit. Let’s assume that the next interest payment date is July 1st and Fred has owned the bond for the first five months of the year and then he sold it to Jackie who has only owned it for about a month come July 1st. What is going to happen on July 1st is that the issuer is going to pay six months of interest to Jackie because she is now the owner of the bond.

Well, that’s not too fair to Fred, right? He’s going to say, “Well, wait, I owned the bond for five months, Jackie has only owned it for a month and she’s going to get a full six months interest payment from the issuer. That’s not fair!” Of course, Fred is right. So that’s why we calculate the Accrued Interest. Jackie would basically have to pay that amount to Fred. It would be added to the purchase price of the bond. But Jackie will know, in about a month, she’s going to get a full six months of interest, which would be the one month interest that she really earned, plus the five months that she’s already compensated Fred for. So the answer would be “C”. Accrued Interest is paid by Jackie to Fred. Now on the exam, you could be required to actually calculate the Accrued Interest, and this would require to figure out the number of accrued days.

One learning point that you want to know is the accrual period goes from the day after the last interest payment date up to, and including, the settlement date … and you may have to do that math on the exam, which means counting out the number of days, which takes practice. But don’t worry. You’ll get lots of practice with that when working with the SeeWhy exam preparation tools. I’m not going to cover actually calculating the number of days in the video. We certainly will if we got a request for it but we do do a great job of covering that in the study guide. Again, you are going to get lots of practice with it with the exam preparation tools, but let’s assume we’ve done that. We figured out that the number of accrued days is 150 days. Let’s do the math because a lot of times when people see another form, in the course, are like, “Oh my gosh, another form that I got to memorize”. Sometimes, they get a little nervous.

This, to me, isn’t really much of a formula. It actually makes a lot of sense. It is intuitive. So, how do we calculate the accrued interest if we’ve already done it? The hard part, which was figuring out the number of accrued days … let’s say being 150, what we do is take a $100,000, which is the face value of the bond. Now we use the face value, not the market value. Remember, the issuer will only pay interest on the face value, which is the amount that they borrowed. We’re going to take $100,000, which is the face value. We then are going to multiply it by 5% and we’re going to get the annual interest payment – as you can see is $5,000. Next let’s divide by 365 days to get the daily interest. I’m getting $13.69 or $13.70 if you want to round up.

Then we just multiplied by 150 days, and we would get an amount of $2,054.79. We’d round up to 80 cents in this case. That is the amount of the accrued interest that Jackie would pay to Fred. I’m assuming it is 150 days. Then, in about another month, she’s going to get the full six months payment. Now, this is a concept that takes a little bit of practice. It is really hard to learn by reading it in a book or a study guide. It is still hard to learn even by video. It’s a concept that you want to get a little practice with and, and when you do, and you do a few of these, it becomes much easier. Thanks everybody. I hope you enjoyed this video lesson. I hope you found it helpful. Keep up the great work and good luck on your upcoming exams.

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