Bonds pay semi-annual interest to their bondholders. When an interest payment is due, the transfer agent pays whoever owns the issuer’s bonds on the interest payment date. The transfer agent does not prorate interest based on how long each investor held the bond during the period, which creates a timing issue.
Assume an interest payment is due on Friday, July 1st. If an investor purchases the bond on Monday, June 27th, they’ll receive the full six months of interest on July 1st, even though they only owned the bond for four days.
It would be unfair if the buyer and seller didn’t adjust for it. In practice, when a bond trade occurs, the buyer pays the bond’s market price plus accrued interest to the seller. The accrued interest compensates the seller for the interest they earned while they held the bond during the current interest period.
To see how this works, walk through this example:
J&J 1 corporate bond trade occurs on Monday, April 10th
J&J 1 = pays interest on January 1st and July 1st
Trade will settle on Tuesday, April 11th (T+1)
The new owner (buyer) will receive the next interest payment on July 1st, which covers the prior six months. But the seller owned the bond for part of that six-month period, so the buyer must reimburse the seller for that portion.
Specifically, the buyer owes the seller interest for the time the seller held the bond from the last interest payment date (January 1st) up to, but not including, the settlement date of the trade (April 11th). That means the buyer owes accrued interest for January, February, and March. On the settlement date, the buyer begins accruing interest for themselves.
A testable point about accrued interest is how days are counted when you count across months. Using the same setup, the trade settles on Tuesday, April 11th. Here are the two common day-count methods.
30/360 method
For example:
A J&J 1 corporate bond trade settles on Wednesday, April 12th. How many days of accrued interest does the buyer owe the seller?
Can you figure it out?
January: 30 days
February: 30 days
March: 30 days
April: 11 days
Overall accrued interest days: 101 days
With the 30/360 method, you assume 30 days for each full month you count over (even if the calendar month has 28, 30, or 31 days). For the month the bond settles in, you count the actual day number up to, but not including, the settlement date.
Actual/365 (a.k.a. actual/actual) method
For example:
A J&J 1 US Government bond trade settles on Wednesday, April 12th. How many days of accrued interest does the buyer owe the seller?
Can you figure it out?
January: 31 days
February: 28 days
March: 31 days
April: 11 days
Overall accrued interest days: 101 days
Although both methods produce the same number of accrued interest days here (101 days), they won’t always match. Two bonds with the same payment schedule and settlement date can produce slightly different day counts depending on the method, though the difference is usually small.
When July 1st arrives, the buyer receives the full semi-annual interest payment from the issuer. The amount the buyer paid the seller as accrued interest is exactly the portion of that payment that belongs to the seller.
With the actual/365 method, you count the actual days in each month. That means you do need to know how many days are in each month. Most people use one of two memory aids.
First, there’s the well-known verse:
Thirty days hath September,
April, June, and November,
All the rest have thirty-one.
February has twenty-eight,
but leap year coming one in four
February then has one day more.
Or, you can use something called the “knuckle method.” Here’s a link to a video describing this system.
The Series 7 can also ask you to calculate the dollar amount of accrued interest. For example:
A $1,000 par, 5%, J&J 1 municipal bond trade occurs on Friday, September 15th. How much accrued interest does the buyer owe the seller?
Can you figure it out?
Answer: $10.69
The last interest payment date prior to September 15th was July 1st. We count from July 1st up to, but not including, the settlement date. With a settlement timeframe of T+1, this trade will settle on Monday, September 18th.
First, calculate the number of days of accrued interest. Because this is a municipal bond, it uses the 30/360 method:
Total = 77 days
Next, calculate the accrued interest owed. This bond pays $50 per year in interest (5% of $1,000). The buyer owes the portion of that annual interest that corresponds to 77 days of a 360-day year:
Now try the same setup with a US Government bond:
A $1,000 par, 5%, J&J 1 Treasury (US Government) bond trade occurs on Friday, September 15th. How much accrued interest does the buyer owe the seller?
How does it look different?
Answer: $10.82
The last interest payment date prior to September 15th was July 1st. We count from July 1st up to, but not including, the settlement date. With a settlement timeframe of T+1, this trade will settle on Monday, September 18th.
First, calculate the number of days of accrued interest. Because this is a Treasury bond, it uses the actual/365 method:
Total = 79 days
Next, calculate the accrued interest owed. This bond pays $50 per year in interest (5% of $1,000). The buyer owes the portion of that annual interest that corresponds to 79 days of a 365-day year:
Both examples follow the same logic, but they produce slightly different answers because they use different day-count conventions. To get these questions right, you need to track:
Most bonds trade with accrued interest, but not all. For example, if a bond settles on the interest payment date, no accrued interest is due. In that case, the seller receives the interest payment for the prior period, and the buyer begins accruing interest for the next period.
Also, zero coupon bonds don’t pay semi-annual interest, so there’s no accrued interest to pay. These bonds trade flat, meaning they trade without accrued interest.
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