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Increasing perpetuity

D

DA Taylor

Member
In one of the assignments there is a question on infinite cashflows, one of which is an increasing annuity. Is there a formula for (Ia)infinity? I do not recall seeing one in the notes and the solution to the assignment question only gives the answer for the annuity without showing any calculations (as they do). Also, if there is a formula for something like this which is not explicitly recorded in the notes and we use it in the exam, will we still get marks for the solution?

Thanks!
 
havent seen the question your talking about

so take lim as n goes to infinity of the forumla for (Ia)n

i.e. lim {(a)n - nV^n}/ i
break it up into

lim (a)n/ i - lim nV^n

so have already seen from perpetuity formula lim (a)n is 1/i

so lim (a)n/i is i ^ -2
and the limit for the other bit is zero since v^n is decreasing faster than n is increasing .exponential vs linear argument. this assumes non zero positive interest rates i think otherwise our sums wont converge , so is i ^ -2 the answer ? it is reassuringly larger than the perpetuity at least .
 
A small correction to the above...

Everything is correct regarding taking the limit as n tends to infinity - it's the initial formula for (Ia)n that's wrong.

(Ia)n = ((a-double dot-n) - nv^n)/i

So, in the limiting process a-double dot-n tends to 1/d, giving the formula for the increasing perpetuity to be 1/id.

And, yes you would get marks for this type of thing - if an exam question related to an increasing perpetuity, I'm not sure I can think of any other approach.
 
lol

Ha , I'm getting quite a collection of wrong answers on this site , Mark is correct I got the formula wrong for (Ia)n the annuity should be an immediate one not an annuity due so put a trema on top.
 
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