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I am currently studying for the actuarial exam FM with the mathematical interest theory textbook from MAA. I have been doing a bunch of problems and the one below is giving me a lot of trouble to figure out. I have tried defining the nominal discount rate in terms of the annual effective rate trying to solve for d. This effort has been fruitless. I stated the problem below two times just to clarify. Any hint that can point me to the direction of solving it will be appreciated.

Given that the nominal discount rate compounded semi-annually minus the annual effective discount rate = .00107584, find the nominal interest rate compounded tri-annually minus the annual effective interest rate.

Given $d^{(2)}-d=.00107584$, find $i^{(3)}-i$

Eleven-Eleven
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user91178
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    Hi, and welcome to MSE. What have you tried and what's giving you trouble? Please indicate your thoughts on the problem so that people can give help that's relevant and appropriate to you. Also, your question is phrased as a command, which some will find rather rude; please consider rewriting this. –  Aug 21 '13 at 03:32
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    Numbers like $0.00107584$ tend to give us math types the heeby-jeebies. Can you restate the problem without any numbers like that? We're mostly okay with $2$ and can bear the occasional $3$. – dfeuer Aug 21 '13 at 03:33
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    Hi, sorry for my post. It is my first time here so I will quickly adapt to form part of the community. dfeur, I tried restating the problem in terms of a discount rate, like d = d(2) - .00107584 then wrote d(2) in terms of d but it did not get me anywhere. – user91178 Aug 21 '13 at 03:58
  • I would use this site for questions of the algebraic and analytic theory of interest while practical problemsolving, i would use the quantitative finance stack site. – Eleven-Eleven Aug 21 '13 at 04:12

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note: $$\left(1-\frac{d^{(2)}}{2}\right)^2=1-d$$ and since you know $d^{(2)}-d=.00107584\Rightarrow d^{(2)}=d+.00107584,$ substitute and you will end up with a quadratic in $d$. Once you know $d$, you can use equalities like the one above to convert $d$ to $i^{(3)}$ and $i$. $$\left(1-\frac{d^{(m)}}{m}\right)^{-m}=(1-d)^{-1}=1+i=\left(1+\frac{i^{(n)}}{n}\right)^n$$ FM is a LOT of disguised quadratics and conversions. Know your identities. It is not as rich a site, but the quantitative finance stack site is much more helpful for aspiring actuaries since the material is all finance.

EDIT: I changed the statement of equality at the bottom to reflect variable $m$'thly and $n$'thly rates since this is the general case.

Eleven-Eleven
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