Literal Equations are what are commonly referred to as formulas, or formulae.  They are recipes for finding the numeric value of a variable, assigned a "letter" name (hence "literal") that typically stands for some sort of real-world quantity, such as Volume, Temperature, Pressure, amount of interest an investment earned, and so on.

This variable has an established relationship to other quantities that are also assigned "letter" names in the recipe (the equation),that gives the relationship between (or among) the quantities.  The deal is, if we know the values for all of the variables in the recipe except one, then we can plug those values into the recipe and solve for the one variable whose value we don't know.

In the above example, you notice that we had a recipe for the accumulated amount, "A", after a certain period of investment.  The ingredients for this recipe are:  the principal (the original amount of the investment); the number of compounding periods per year; the number of years of the investment period; and the rate of interest.

NOW, consider this:  Since this recipe depends on the relationship between "A" and its ingredients, we can use this relationship to make a recipe for any of the ingredients of "A" also.  So let's suppose that "A" is known, but one of the ingredients, say "P," is not.  Then we need a recipe for "P."  How to get it?  Well, since "P" is our unknown, let's take the recipe for "A", consider all of the ingredients (including "A") as known quantities, and solve it for "P".    That is, get "P" all by itself on one side of the equation.  Then, PRESTO, we have a recipe for "P".   The process will go like this:

which is the recipe for P that we wanted.

Now, with this recipe, we can solve problems like:

• PROBLEM:  I need to have $50,000 in ten years' time.  If I can get an interest rate of 6%, compounded monthly,
                        how much money would I have to invest now?
  
  

• SOLUTION:  We know that we are wanting to find the quantity P, so we know that we need to use the recipe for P.
                         So we check the problem to make sure that we have all the ingredients:

  • A is the amount we want to have at the end of the investment period, so A is $50,000

  • r is the annual interest rate, so r is 6%, or 0.06.

  • n is the number of compounding periods per year, so n is 12 (12 months per year)

  • t is the number of years of the investment period, so t is 10.
    

  Yes, we have all the ingredients, so we are ready to put them into the recipe for P, and we get
  
  

   

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This  is what is known as working with literal equations....solving them for one or the other of the "letter" quantities involved.

And you can do this for any of the "letter" quantities for which you need a recipe:

• Example 1:
  
  

• Example 2:
  
  

Click on to go to :    top of page            Solving for P           Example 1          Example 2