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Fixed Income -- Par curve algebra
It has been over 25 years since I tool an algebra course and I am stumped (and annoyed at the CFA Institute curriculum for not clarifying). In reading 53, section 4 dealing with par curves, the curriculum lays out equation 13 (100 = PMT/(1+Z1) + PMT/(1+Z2)^2 + ... + (PMT+100)/(1+ZN)^N) and says "the problem is to solve for PMT algebraically." Yeah, no kidding. But it doesn't show its work. It just cavalierly declares what the answer is. From what I can tell, there is no shortcut way to do this like with YTM on the 12C. You just have to brute-force your way through it. I am tempted to blow it off, given that there will probably be at most 1 question on it and I don't want to spend a whole day trying to figure it out. Can someone please show me the algebra? I'm sure it's easy and I'll feel silly for asking. But I am starting to get frazzled and it is affecting my ability to continue studying.
Thanks,
BW
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Answers
Sorry if I wasted anyone's time.
"Never half-ass two things. Whole-ass one thing."
If the Z terms are not the same, the TVM functions won't help you since they only allow for 1 discount rate. You need to set up the equation in terms of each period's discount rate.
Prash, you can't use the TVM functions of an HP12C for problems with more than one discount rate.