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# Advanced Math/Price Formulae - which is correct?

Question
Dear Scott,

No problem. I have been all expert for many years and some times work just gets on top of you. I have marked this question as private because of the commercial overtones and also the possibility that you might wish to charge me for the work, but you can make it public if you wish.  Now for the problem

* means multiply and / means divide.

I have two formulae which purport to calculate the effect of currency fluctuations and price inflation on payments to a contractor.  The contractor does an amount of work in a month.  The value of this work will be adjusted to account for fluctuations in the exchange rate and for changes in the price index (such as the consumer price index).  The Contractor works in one country, say Afghanistan, and he gets paid in another currency, say US\$, rather than the local currency.

First Formula   Dm = Qn * C * Po * (Txo/Txn)*(In/lo - 1)
The terms are defined as :-
Dm=     increase or decrease to be paid for the material concerned by the revision of prices during the month "n".
Qn=     quantity of works carried out during the month n involving one or more of the materials in question.
C=      coefficient of transformation allowing to calculate the quantity of material used in the quantity of works carried out Qn.
The value of coefficient C is defined as follows:
for cement, the coefficient  C is expressed in tonnes for each cubic metre of concrete executed as per category specified in the contract;
for reinforcing steel, the coefficient C is expressed in tonnes of steel laid for each cubic metre of reinforced concrete executed in accordance with the plans of reinforcement;
for bituminous mixtures, the C coefficient is expressed in tonnes of  bitumen specify the bitumen category PEN 76-10 performance grade for tonnes of bituminous mixture executed.
Po=     price of material to be revised as contained in the Contractor's tender.
Txo=    exchange rate between the currency of contract payment and the currency of the material's country of origin at the reference date.
Txn:    exchange rate between the currency of contract payment and the currency of the material's country of origin at the month n.
Io=     Official index of the material at the reference date.
In=     Official index of the material at the date of purchase.

Second Formula  Dm= Q*c*P0*[(Matn/Mat0)*(Txn/Tx0)-1]
The terms are defined as :
Dm, Q & C as above
Po=     price of material to be revised as contained in the Contractor's tender.
Tx0 =   exchange rate between the currency of contract payment and the currency of the selected indicator at the reference date.
Txn =   same exchange rate at the month n.
Mat0=   official supply price of the concerned material at the reference date.
Matn=   official supply price of the concerned material at the month n.

I have tried to decide which one is accurate, but it is beyond me.  My son suggests keeping one set of variables constant and then the other, but I am not sure how to do it.  I have tried building an array in Excel to see what happens, but no luck.  There appear to be two major difference - one in the ratio Txn/Tx0 in one and Tx0/Txn in the other.  Another difference is the location of the term '-1'.  I hope that I have expressed it clearly.

Help, please, which formula represents the true effect of the price variation of the goods?

It all depends on the product in que I have seen that the only difference in the two equation is that the 2nd equation has (Matn/Mat) in it.  If the price does not vary accorrding the price varies depending on the quantity there is, then the second one should be used.

Volunteer

#### Scott A Wilson

##### Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

##### Experience

Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.