Sometimes a discounted note is issued rather than an interest-bearing note. Why would a someone do this rather than the standard interest bearing note? What are the pros and cons of doing so? Who would issue a discounted note?

I am starting to answer your question from backwards

WHO: Generally Discounted Notes are issued by the Govt.

WHY: Assume a Govt decided to take a big infrstructure project which is financed by issuing Discounted Note of $ 80 redeemed after 5 years at face value of $ 100. The Govt decided to issue discounted note because it has shortage of finances in the intitial years.

The Govt is not desiring to put additional pressure of interest in intitial years... rather postponed it until agreed period.


The second imporatant consideration is Present Value of Money

Suppose a firm gives two options to investor :
OPTION 1 Issues discounted note at $80 redeemable at a premium of 10% i.e. $110
OR
OPTION 2 Issue a 4 % Interst bearing note for 5 years redeemable at par

Comparison
OPTION 1 Total interest = 20 Premium = 10 Total earning = 30
OPTION 2 Total Interest = 20 Premium = 0 Total earning = 20

Fruther assuming discounted rate = 10 %
Year 1 = 0.909
Year 2 = 0.826
Year 3 = 0.751
Year 4 = 0.683
Year 5 = 0.621
TOTAL = 3.79 (SUM OF YEAR 1 TO YEAR 5) to calculate interest annuity

Now since in option 1 The money is received after end of year 5

Present value = $ 110 * 0.621 = $68.31

and in OPTION 2

At 4% annual interest shall be $ 4 each year.
the present value of interest (an annuity for 5 years ) shall be
$4 * 3.79 =$15.16

(+) Maturity value of principal amount at the end of 5th year shallbe
$100 * 0.621 =$62.10

TOTAL EARNING ( OPTION 2) = $15.16+ $62.10 = $77.26

Now you can analyse from the above the benefits of issuing DISCOUNTED NOTES

These are fool proof instruments :

Good answer still a little confused