Suppose there's a five year bond that pays an annual coupon of 2.4%, and it currently trades at a yield of 2.43%.

The bond has exactly five years remaining until maturity, and the last coupon has just been paid since. There is no accrued interest on the bond at the moment.

The clean price is the same as the dirty price, and it can be calculated using the standard yield to maturity formula, which discounts future cash flows. Back to today. Using the yield to maturity as the discount rate, the calculated price would be 99.8603%, and this is both the clean and the dirty price because the coupon was just paid.

Now, let's assume that on the next business day, the yields maturity remains unchanged at 2.43%.

However, since one day has passed, the dirty price now needs to include one day of accrued interest, and it's slightly increased to 99.8669%.

To calculate the clean price of this bond, we first need to determine the accrued interest, and then we can just subtract it from the dirty price.

Using the actual actual day count convention, and assuming a non-LEP year, we can calculate the accrued interest by multiplying the coupon rate of 2.4% by one over 3 6 5.

When we subtract this accrued interest from the dirty price, we arrive at a virtually unchanged clean price of 99.8603%, so the dirty price of the bond has increased slightly due to the accrued interest of one day.

While the clean price remained practically unchanged, the clean and dirty prices would behave as shown here.

Assuming a constant yield to maturity over the life of the bond, the clean price will remain relatively stable over time, especially if the bond initially trades near par value while the dirty price follows a sore tooth pattern.

As time progresses, the dirty price increases reflecting the accumulation of accrued interest.

This increase is linear over time and continues until the next coupon payment date.

On the coupon payment date.

For example, at the end of year one, a bond holder receives the coupon payments, which includes the accrued interest.

Consequently, the accrued interest resets to zero, and the dirty price drops back down to the level of the clean price.

This cycle repeats with each coupon period until the bond reaches maturity.