Calculating Accrued Interest on a Coupon Bond

Assume you are buying a bond with a 6% coupon that pays semiannually and want to ensure you do not pay too much accrued interest. The bond last made a coupon payment 35 days ago and has 180 days in a period. What is the accrued interest owed to the seller for a $1,000 investment?

Incorrect. The coupon is split between two payments over the course of a year.

Assume the 6% semiannual bond pays interest on January 30th and July 31st. 131 days have passed since the last coupon payment, and there are 182 days in the period. The bond has a day-count convention of 30/360. What is the accrued interest if you invest $1,000 into the bond on June 10th?

Incorrect. This calculation would be for a $100 investment and a 6% annual coupon.

Incorrect. The bond makes two interest payments over the course of a year. This means that you must divide 360 by the payment periods.

Incorrect. This calculation does not use the 30/360 day count.

If the bond only paid interest once a year, what would be the accrued interest on an actual/actual day-count convention?

Correct! $$\displaystyle \$ 60 \times \frac{131}{365} = \$ 21.53 $$ On a bond that pays annually, the full annual coupon is multiplied by the actual days that have passed divided by 365 days in the year.

Incorrect. This calculation matches a 6% bond that pays interest twice a year.

Incorrect. Remember, this calculation is for a 30/360 day count.

In summary: [[summary]]

__Accrued interest__ is the proportional share of the coupon that has been earned since the last coupon payment. If you were to buy a bond that is between coupon payments, you would owe the interest that has accrued since the coupon payment to the seller on the settlement date. You can calculate accrued interest with the following formula: $$\displaystyle \text{Accrued Interest} = \text{Payment per Period } \times \frac{\text{ Days since last payment}}{\text{Days in the period}}$$

Great job! Since the bond pays the 6% annual coupon in two payments, only half of the coupon is paid each period. If you find it difficult to remember how to split the coupon, it might be easier to remember the accrued interest (AI) formula as $$\displaystyle \text{AI} = \text{Payment per Period } \times \frac{\text{ Days since last payment}}{\text{Days in the period}}$$ $$\displaystyle \text{AI} = \frac{60}{2}\times \frac{35}{180} \approx 5.83$$

When you celebrate a birthday, 365 days have passed since the last time your age changed (excluding leap years). However, a calendar year is not always how accrued interest is calculated. Depending on the country in which a bond is issued or the type of bond, accrued interest can be determined by different day-count conventions. There are several day-count conventions used around the world. Luckily for you, the CFA® curriculum only covers two types of accrued interest calculations: 30/360 and actual/actual. __30/360__ calculates interest as 30 days in a month, regardless of how many actual days are in the month. 30/360 also shortens the number of days in a given year to 360. __Actual/ actual__ uses the exact number of days in each month and days in a year. They also call this the "government equivalent yield."

Great job! $$\displaystyle \frac{\$ 60}{2} \times \frac{130}{180} \approx \$ 21.67 $$

$1.17

$5.83

$11.67

$10.83

$21.59

$21.67

$21.53

$21.59

$21.67

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