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Fixed Income -- Par curve algebra

bjw699bjw699 Long Beach, CAPosts: 7 Associate
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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