Hello,I found out those four formulas to quote bond YTMs. Do you know which formula is applied in which case? Apparently it depend on local market conventions and time to expiry...- simpleP = cp1 / (1+y*t1) + cp2 / (1+y*t2) + ... + N / (1+y*tn)- compoundP = cp1 / (1+y)^t1 + cp2 / (1+y)^t2 + ... + N / (1+y)^tn- "mixed"P = cp1 / (1+y*t1) + cp2 / (1+y)^t2 + ... + N / (1+y)^tn- plainP = (cp1 + cp2 + ... + N) / (1+y*tn)ti is the number of years from evaluation to coupon date.thanks !

The formula P = (cp1 + cp2 + ... + N) / (1+y*tn) makes no logical sense at all as it applies the same discount factor to cash flows that occur at different times. Never saw that in a book but if I did I would only chuckle as it reveals nothing useful. (By the way, you must mean that N is the return of principal at maturity, otherwise none of the formulas you reported make any sense)In general, when bonds have one coupon till maturity remaining many systems treat them as money market instruments using simple interest. Bonds with more than one coupon remaining are generally discounted using compound interest for all cash flows.What you call the "mixed" method is also called the "Treasury" method in the US and the "Moosmuller" method in Europe. The next coupon payable after settlement is discounted using simple interest and later cash flows using compound interest. It is pretty much a curiousity and is not quoted in the market place.The industry standard "Street" method discounts all cash flows using compound interest (with the caveat noted above for short-dated bonds).

Thank you DavidJN !The first formula P = (cp1 + cp2 + ... + N) / (1+y*tn) is actually used as a way to quote YTM for Japanese Governement Bonds. This is the only usage I am aware of.