Hi All,

What is the different between add-on and discount in calculation?

Example:

The following are 90-day money market instruments:

Instrument A=Quote: 5.78%, 360 days, discount rate

Instrument B=Quote: 5.96%, 365 days, add-on rate

Which has the highest rate of return?

Thank you so much in advance if you can help me understand this.

Hello,

Is the answer- Instrument B?

What we are required to do basically is to convert either one of them to be of the same quotation as the other i.e. Convert Instrument A from Bank Discount Yield (" **BDY**") to Add-On Rate (" **AOR**") or vice-versa for Instrument B. In my working below, I will convert BDY of A to AOR.

The formula for **BDY is = [(P1-Po)/ P1] * (360/t)** where P1 is the par value of the instrument, Po is the current value of the instrument and t is the duration of the instrument

We are given that BDY is 5.78% and we know P1 (we can assign a arbitary value of 100 or 1,000 ) and we need to solve for Po.

Equating the above equation to 5.78% we obtain a value of **98.555** for Po.

Next we will determine the AOR for Instrument A. We know that Instrument B is quoted as AOR on a 365 days basis. This basically means:

*AOR= [(P1-Po)/ Po] * (365/t)*

*Note that now the denominator is Po instead of P1*

AOR can be quoted on either a 360 days or 365 days basis.

If you now plug the values into the AOR formula you will get: **5.9462%** ( < 5.96%)

Hope it helps!

Cheers,

Ernest

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