# example regarding zero coupon bonds

This example is from Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by Carmona, René, Tehranchi, M R.

I am wondering if the calculation is correct?, he says approximately, but I am wondering if you agree with me in that the calculation of the discount is to be calculated like this: ?

$100000-100000/(1+r) = 100 000 *[1- 1/(1+0.06/4)]=1477.83$

And that he he pays at the start: $100000/(1+0,06/4)=98522.17$. Or shall the calculations be done as in the example? Here is the example:

You have to be very careful with terminology here. In particular "yield" is being thrown around carelessly by both of you.

The textbook is correct if the (meaningless) phrase "at a 6% yield (rate)" is crossed out and replaced by "at a 6% discount rate". And this is how Tbill's are handled when they are issued (the press release by the US Treasury speaks of discount rate http://abcnews.go.com/Business/wireStory/rates-us-treasury-bills-fall-weekly-auction-40174524) and in the secondary market.

The calculation you are doing is correct if you are assuming "a 6% money market yield" and then calculating the price from that. And money market yield (as well as "bond equivalent yield" a related measure) are useful measures that are closer to the everyday meaning of "yield", i.e. how much money you make per year. The MM yield and BE yield are what is used in analytical work (for example to compare tbills to other securities).

The real world calculations of yields involve hair splitting details (such as 360 vs 365 day basis, leap vs non-leap years,...) that are best left out of a general textbook and so just consider this an an approximate example without sweating the details.