Is there an offiical formula for calculating add-on rate? Please see the question below:

The add-on rate assuming a 365-day year of a 270-day banker’s acceptance quoted at a discount rate of 4.4% for a 360-day year is closest to … ?

I get confused by so many day quoted stuff like 365, 270, 360. I am not sure how I should go about it? Thanks!

First you have to determine both the P_{1} (the face of the instrument) and P_{0} (the selling price of the instrument)

We know that Bank Discount Yield (“ **BDY** ”) is given by the formula:

[(P_{1 }– P_{0 })/ P_{1 }] * (360/t), where t= duration of holding the instrument.

We have that 270 days banker’s acceptance (“ **BA** ”) with t= 270 days,

[( **100** – P_{0 })/ **100**] * (360/ **270** ) = 4.4%

Solving for P_{0 }we obtain: 96.7

With this information, we can now proceed to computing the add on rate (“ **AOR** ”) based on a 365 days basis:

[(P_{1 }– P_{0 })/ P_{0 }] * ( **365** /t), noting that the days is 365 instead of 360.

Applying the values we have:

[(100 – 96.7 )/ 96.7] * ( **365** /270) = 0.0461 = **4.61%**

In summary, money market instruments are quoted using BDY or AOR; using a 360-days/365-days basis. AOR quoted using 365-days basis is aka Bond Equivalent Yield.

Hope the above helps.