54d: calculating accrued interest in a bond

We have a 5% bond that pays a semiannual coupon, which is $25 every six months. YTM is 4%, so that’s 2% per pay period.

A) The calculated value on the day of the most recent payout is $1019.04.

B) 67 days into the next period, we sell the bond for $1026.46. The way we got this figure is we did

1019.04*1.02 ^(67/183) = $1026.46.

C) In essence, the bond gained _1026.46-1019.04= $7.42 in interest _ over the course of 67 days.

D) Why then, does the book claim that the bond accrued $9.15 in interest during those 67 days?

Because AI= t/T* coupon. 67/183*25.

Accrued interest is calculated at a constant rate per day; in this case, it’s $25 × (67/183) = $9.15.

So on the 67th day, what if they ask for the “flat price”?

Is it possible that the flat price is going to be less than the par value?

Flat price is the quoted price, it can be less than par, it can be at premium, whatever. AI changes, flat price doesn’t(shouldn’t, to the best of my knowledge).

The flat price will change with theYTM and time till maturity, and accrued interest will change with time. If YTM is higher than the coupon rate, the flat price will be less than par (and vice-versa).