Between coupon dates: accrued interest, flat and full price

In short

• Full price (invoice or dirty price) = flat price (quoted or clean price) + accrued interest (AI).
• The buyer pays the full price on the settlement date; dealers quote the flat price.
• $AI = (t/T) \times PMT$: t = days since the last coupon, T = days in the coupon period.
• Actual/actual counts real calendar days; 30/360 treats every month as 30 days and the year as 360.
• $PV^{Full} = PV \times (1+r)^{t/T}$, where PV is the price at the last coupon date.
• AI does not depend on the YTM; only the flat price reacts to a change in rates.