Actuarial Outpost PV of a geometric increasing annuity due
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#1
04-12-2012, 11:15 AM
 MathandBikes Member SOA Join Date: Feb 2012 Favorite beer: ESB Posts: 549
PV of a geometric increasing annuity due

Question:

You make investments at the beginning of the year for 30 years starting at \$100. Each payment after the first increases by 10 percent every year. Interest is calculated at 12 percent per year. Find the present value of this annuity.

(This is my own question that is similar to a question I saw on ADAPT)

My Solution:

v(Ia)angle30 for a geometric immediate.

100 (1/1.12) ((1-(1.1/1.12)^30)/(.12-.1)) = 1864.17

Is this correct? Thanks.
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#2
04-12-2012, 11:32 AM
 DanielMena9 Member SOA Join Date: Feb 2012 Location: Maywood Studying for Enjoying Senior Year! College: 3rd Year UCSB Favorite beer: Coconut Water Posts: 96

I would have to say it is not correct?

the solution is

100*[1+(1.1/1.12)+(1.1/1.12)^2+....+(1.1/1.12)^29]

= 100{ [1-(1.1/1.12)^30]/[1-(1.1/1.2)] }

= \$2,338.42

similarly,

100* a double dots angle 30 with i'=(.12-.1)/1.1
again = \$2338.42

where i' is the real interest rate
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#3
04-12-2012, 11:35 AM
 FreeYoMind Member SOA Join Date: Sep 2011 Studying for MLC Posts: 89

I arrived at the same answer as Daniel. Instead of discounting the annuity you need to bring it forward one period.
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#4
04-12-2012, 11:46 AM
 MathandBikes Member SOA Join Date: Feb 2012 Favorite beer: ESB Posts: 549

Right right, thanks all.

Got my mistake now. I'm not sure why I was discounting the thing. Make the mistakes now I guess! Hopefully they won't happen on test day.
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