Actuarial Outpost Increasing Perpetuity problem.
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 Financial Mathematics Old FM Forum

#1
11-10-2017, 03:49 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128
Increasing Perpetuity problem.

My approach:

$v^{n}(\frac{1}{i}+\frac{1}{i^{2}})= v^{n}(\frac{i+1}{i^{2}}) = v^{n}(\frac{1}{di})$

I got answer E but the answer is D. What did I do wrong?
#2
11-10-2017, 04:16 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,120

Quote:
 Originally Posted by Futon My approach: $v^{n}(\frac{1}{i}+\frac{1}{i^{2}})= v^{n}(\frac{i+1}{i^{2}}) = v^{n}(\frac{1}{di})$ I got answer E but the answer is D. What did I do wrong?
You are doing an n-year deferred increasing perpetuity immediate, and you have an n-year deferred perpetuity due, or an n-1 year deferred perpetuity immediate.

Last edited by Gandalf; 11-10-2017 at 04:27 PM..
#3
11-10-2017, 04:30 PM
 NattyMo Member Non-Actuary Join Date: Nov 2016 Posts: 606

Quote:
 Originally Posted by Futon My approach: $v^{n}(\frac{1}{i}+\frac{1}{i^{2}})= v^{n}(\frac{i+1}{i^{2}}) = v^{n}(\frac{1}{di})$ I got answer E but the answer is D. What did I do wrong?
Try doing the "present" value at time n first.

$V_n = 1 + 2\nu + 3\nu^2 + 4\nu^3 + \dots$
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#4
11-10-2017, 04:31 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Gandalf Think about the first term of your expression. It is $v^{n}(\frac{1}{i})=v^{n+1}$The first payment is at the end of n years, so that can't be right.
Thanks. Multiplying my setup by v^-1 gave me the right answer.
#5
11-10-2017, 04:32 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by NattyMo Try doing the "present" value at time n first. $V_n = 1 + 2\nu + 3\nu^2 + 4\nu^3 + \dots$
Yup, apparently I discounted all the way to time 0 and I still used the formula for perpetuity immediate instead of due.