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 Financial Mathematics Old FM Forum

#1
04-21-2019, 02:45 AM
 ms556a SOA Join Date: Mar 2016 College: Illinois Central College Posts: 8
Problem help

I have a question could I please get some help from the pros.

A liability has a present value of 300,000 at 4.5% effective. The modified duration of the liability at 4.5% is 10. Let X = the present value of the liability at 4% effective using the first order modified approximation. Let Y = the present value of the liability at 4% effective using the first order Macaulay approximation. Determine X-Y.
#2
04-21-2019, 01:22 PM
 Dr T Non-Fan Member SOA AAA Join Date: Sep 2001 Location: Just outside of Nowhere Posts: 96,828

42

There is probably a specific exam forum to ask this question. Not the General Actuarial Forum.
If someone knows which one, I can move it there.
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#3
04-21-2019, 02:05 PM
 Moderator1 Moderator Join Date: Sep 2001 Posts: 16,060

I took a guess that it belongs here. OP can move it again if he’s taking something else.
#4
04-22-2019, 08:07 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 6,121

Quote:
 Originally Posted by ms556a I have a question could I please get some help from the pros.
I don't often help with what looks like homework, but here goes ...

Quote:
 A liability has a present value of 300,000 at 4.5% effective.
What does that mean? There are lots and lots of possibilities for the cash flows.

Quote:
 The modified duration of the liability at 4.5% is 10.
What does that mean? Combined with the previous constraint, is there a unique cashflow that would work? (Ans: no)

Notice, that below there are no more givens. So, assuming the problem is doable, it can't matter what cashflows you pick, provided that the PV (at 4.5% effective) is 300K and the modified duration at 4.5% is 10.

Can you find an especially simple such cashflow?

Quote:
 Let X = the present value of the liability at 4% effective using the first order modified approximation. Let Y = the present value of the liability at 4% effective using the first order Macaulay approximation. Determine X-Y.
Compute X-Y for your simple cashflow --- if the problem is doable, that will give you the right answer.
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#5
04-25-2019, 12:08 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,927

Do you have the study note on duration from the FM syllabus? The necessary formulas are in there. It as a straight plug the numbers in question.
#6
05-12-2019, 09:12 AM
 xkang1129 SOA Join Date: Mar 2019 College: University of Missouri St Louis Posts: 6

Just need to plug in the values into the formulas, should be pretty straight forward