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  #1  
Old 11-20-2017, 05:37 PM
Futon Futon is offline
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Default Perpetuity question

The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i.
Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01.

Calculate R.
(A) 1.23
(B) 1.56
(C) 1.60
(D) 1.74
(E) 1.94

My approach:











Since the first payment is at t=2, I want the perpetuity formula to be at t=0 or t=3. I chose t=3.





What did I do wrong?

Edit: Answer is D

Last edited by Futon; 11-20-2017 at 06:34 PM..
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  #2  
Old 11-20-2017, 06:24 PM
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When you post questions, post what the author says the answer choice is.
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Old 11-20-2017, 06:34 PM
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Sorry about that. Answer is D
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  #4  
Old 11-20-2017, 06:48 PM
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Your calculations look OK to me. What's the source of the question?
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Old 11-20-2017, 06:51 PM
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Quote:
Originally Posted by Gandalf View Post
Your calculations look OK to me. What's the source of the question?
This is one of the questions from the sample SOA exams. I think should've included the solution as well, sorry:



This solution does nothing for me. I do not understand why they are discounting the second perpetuity back by a year making the perpetuity at time = 1.

Also that mysterious "+1".

It's a very unintuitive solution imo.
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Old 11-20-2017, 08:54 PM
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Their solution is correct. Yours has the payment in the 3-year annuity at the end of year 2, not the beginning. The payment is at t=1, not t=2.
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Old 11-20-2017, 09:55 PM
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Quote:
Originally Posted by Gandalf View Post
Their solution is correct. Yours has the payment in the 3-year annuity at the end of year 2, not the beginning. The payment is at t=1, not t=2.
Ah right. "beginning of year two" blinded me. Why the +1 though? I would've multiplied by (1+i)^3 in addition to (1+i)^-1 since it is a perpetuity-due. Is there a reason why he didn't do that?
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Old 11-20-2017, 11:54 PM
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Either is fine. Thinking of the every year case, you can do either:

perpetuity-due = perpetuity-immediate + 1
or
perpetuity-due = (perpetuity-immediate)(1+i).

Neither formula is more right than the other.
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  #9  
Old 11-21-2017, 12:09 AM
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Quote:
Originally Posted by Gandalf View Post
Either is fine. Thinking of the every year case, you can do either:

perpetuity-due = perpetuity-immediate + 1
or
perpetuity-due = (perpetuity-immediate)(1+i).

Neither formula is more right than the other.
Thank you
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