# GuideAccrued Interest

**What is accrued interest?**

**Accrued interest** is that **part of the coupon income** that becomes relevant when an investor buys or sells a bond **prior to it's maturity date**.

Accrued interest is **calculated** from the **previous coupon date** to the **settlement date** of the bond. A **seller receives** accrued interest, whereas a **buyer pays**.

An alternative explanation could be that if a bondholder decides to **sell** a bond **before** it pays the **next coupon**, part of the accumulated coupon income since the **previous coupon date** will still be collected by the seller. This part is called “accrued interest”.

**Five** components are needed to calculate the exact amount of accrued interest:

- The previous coupon date
- The bond's settlement date
- The nominal amount invested
- The coupon rate itself
- The so-called "day-convention"

For example, say an investor holds a Eurobond that pays a coupon twice a year, or semi-annually, and is held for 110 days since the previous coupon date. The bond follows a 30/360-day convention, meaning a year is assumed to have 360 days and a month 30 days. In the event of a sale of the position and given that this bonds pays a coupon every 180 days (semi-annually), the holder will receive the 110/180-day part of the coupon. It is said that the investor “gives up” the remaining 70 days.

It is important to stress that accrued interest is based on the **settlement date** and not on the trade date. For example, if a bond **settles** a day after the coupon date, there will be 1 day of accrued interest. Also, when a bond settles on the coupon date, the buyer will not pay any accrued interest and the seller receives all (i.e. the coupon).

Accrued interest is **added to the principal amount (nominal amount multiplied by clean cash price)** to determine the total cash amount of the transaction. Alternatively, accrued interest can be quoted as a price component and added to the clean price to state the so-called **"dirty price"**.

**What is the difference between a clean and a dirty price?**

**Bond prices** are always in **percentages**, but we tend to drop the percentage sign in a quote. So, 98.50 is effectively 98.50%.

Also, Eurobond prices are always quoted **“clean” of the accrued interest** component. When we add the accrued interest part to the price, we get the **“dirty price”**.

Clean Price | 90 | Quoted price excluding accrued interest |
---|---|---|

Accrued interest | 3.071181 | Accrued Interest / Nominal Amount x 100% |

Dirty Price | 93.071181 | Clean Price + Accrued interest |

**How is accrued interest calculated?**

In order to calculate the correct total amount of accrued interest, **a day count adjustment** is needed when determining the **number of days between the last coupon date and the settlement date**. This adjustment follows the **day-count convention** set out for the bond.

For a 30/360-day count convention, the adjustment ensures that each calendar month has 30 days and each calendar year has 360 days. For instance, calendar months such as December (31 days) or February (28/29 days) are both reset to have 30 days under the 30/360 day-count convention.

We can use the below example to illustrate the day count convention adjustment.

Day Count Convention | 30/360 | We assume 30 days for every month and 360 days for every year |
---|---|---|

Coupon Frequency | Semi-Annually | |

Trade Date | April 14th 2020 | |

Settlement Date | April 16th 2020 | |

Previous Coupon Date | November 21st 2019 | |

Days since Previous Coupon | 145 days | (Settlement Date - Previous Coupon Date) +/- Day Count Convention Adjustment |

Next Coupon Date | May 21st 2020 | |

Days to Next Coupon | 35 days | (Next Coupon Date - Settlement Date) +/- Day Count Convention Adjustment |

A total of exactly 147 calendar days has passed since the Previous Coupon Date up until the Settlement Date.

The bond’s coupon schedule follows a 30/360-day count convention and therefore we need to adjust the total number of calendar days to 30 for months in this period. This means that the months of December (31 days), January (31 days), February (29 days) and March (31 days) all need to be reset to 30 days. This translates to an addition of 1 day to February and a subtraction of 1 day for December, January and March. The total adjustment is therefore -2 days and the total of 147 calendar days needs to be adjusted to 145 days instead. No day adjustment is needed to calculate the days to the Next Coupon Date as the month of April already counts 30 days.

Once we have successfully determined the days the bond has been held since the last coupon date, we multiple the below components to calculate total accrued interest:

Nominal Amount | $1,000,000.00 |
---|---|

(Coupon Rate / Coupon Frequency) | (8.00% /2) |

(Days passed since Previous Coupon Day / Assumed Number of Days in Year as per Day-Convention) | (145 days/360 days) |

Total Accrued Interest | $16,222.22 |