# Accrued Interest Mini-Lesson

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I want to talk about a concept called accrued interest. 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. Let’s look at a question together.

Jackie is about to retire and requires regular income. As a result, she decided to purchase a bond with a fixed coupon rate of 5%, a \$100,000 face value in the secondary market from Fred and paid a market value of \$105,000. Upon the sale of the bond, what is true of accrued interest?

a) Accrued interest is paid by Fred to Jackie
b) Accrued interest is paid by Jackie to Fred
c) Accrued interest is paid by the issuer to the Jackie
d) Accrued interest is paid by the issuer to the 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? The actual answer may surprise you. 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, “What do you mean? 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. 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 work through this concept. 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, He then he sold it to Jackie, who has only owned it for about one month by the time the interest payment is made on July 1st. On July 1st, 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 fair to Fred, right? He’s going to say, “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 month’s interest payment from the issuer? That’s not fair!” Of course, Fred is right. So that is why we calculate the accrued interest. Jackie would basically have to pay that 5-month’s worth of interest to Fred, and 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 again, the answer is “b”. Accrued interest is paid by Jackie to Fred.

On the exam, you could be required to actually calculate the accrued interest, and this would require you 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 will 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 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. Let’s assume that the number of accrued days is 150. Let’s do the math because a lot of times when people see another formula in the course, they think, “Oh my gosh, another formula that I have to memorize?” Sometimes, they get a little nervous.

To me, this 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? First, we’re going to take the \$100,000 face value, and multiply it by the 5% coupon rate, and we get the annual interest payment of \$5,000. Next, we divide that by 365 days to get the daily interest of \$13.70. Then we just multiply this by 150 days, and we get an amount of \$2,054.79. That is the amount of accrued interest that Jackie would pay to Fred. Then, in about another month, she’s going to get the full six month’s payment of \$2,500.

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 (or a video transcript). It is still hard to learn even by watching the video. It is 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.