Add-On Rate (AOR)

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 P1 (the face of the instrument) and P0 (the selling price of the instrument)

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

[(P1 – P0 )/ P1 ] * (360/t), where t= duration of holding the instrument.

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

[( 100 – P0 )/ 100] * (360/ 270 ) = 4.4%

Solving for P0 we obtain: 96.7

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

[(P1 – P0 )/ P0 ] * ( 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.