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#1




Fm question
A perpetuity has payments of 1, 2, 1, 3, 1, 4, 1, 5,… Payments are made at the end of each year. You may assume an annual effective interest rate of 5%. Determine the present value I this perpetuity.
I know this problem was discussed before but I’m stuck. How do I do this? I set up my time line at time 1 payment is 1, time 2 payment is 2, time 3 payment is 1, time of 4 payment is 3, and so on. What do I do now? 
#3




You have to split it up in ways you can evaluate. Here are two possibilities:
Payments of 1 every year, and payments of 1 at time 2, 2 at time 4, 3 at time 6, etc. Or Payments ok 1 at times 1, 3, 5, ..., and payments of 2 at time 2, 3 at time 4, 4 at time 6, etc You ought to know how to evaluate any of those 4 patterns, and should be able to convince yourself that either way of splitting gives the same answer. 
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#7




For each option, you can decompose the ugly looking payment streams into simple, closed form solutions.
Option 1: Yes, you get 1 forever assuming no increases. The extra bit is an increasing perpetuity that bumps up every 2 years instead of every 1 year. Option 2: This has similarities to option 1. You get 1 every 2 years forever and in the "off" years, you get an increasing perpetuity every 2 years. Ninja'd.
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"I'm tryin' to think, but nuthin' happens!" Last edited by Breadmaker; 11042018 at 08:43 PM.. Reason: Ninja'd by Gandalf 
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