Financial: Multi-letter Variables
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Understanding that we like to talk about present value
and future value, it should not seem too strange that we want to represnt these by
symbols that relate to those two names.
In fact, we like to use PV for present value and
FV for future value.
The only problem with this is that until now, at least in algebra and
absolutely in our programs on the TI-83/84 calculators we have only used single letter variables such as
x, or I, or R, or T.
With single letter variables when we see PRT we "understand" that
we have implied multiplication and that PRT really means
P*R*T. Once we allow multi-letter variables, such as PV then
that understanding of implied multiplaction has to be forgotten.
After all our "principle times rate times time" cannot just be written as PVRT
because someone might assume that means P*V*R*T. Therefore,
for the rest of the discussion of financial calculations we will have to be careful to use "implied
multiplication" only where there will not be confusion.
When we introduced the terms present value and future value we looked at a problem
stated as:
With a present value of $4000, and a simple interest rate of 5% for 3 years,
what is its future value?"
We can capture that as a mathematical statement via
FV = PV + I
where I
is the interest earned. But we know that
I = PV*R*T.
Therefore, we can restate the first equation as
FV = PV + PV*R*T
Going back t our algebra skills we can factor that to give
FV = PV*(1 + R*T)
which we could have written as
FV = PV(1 + R*T)
because the one implied multiplication is not confusing.
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©Roger M. Palay Saline, MI 48176 March, 2017