Several years ago there was an entertaining movie made called “Peggy Sue Got Married”. The plot concerns Peggy Sue who, as the movie begins, is attending her 25th high school reunion. Suddenly, due to some ripple in the fabric of space-time, she is thrust back to her high school days. So, the rest of the movie is mainly about the adventures of a seventeen year old high school student with the life experiences of a middle-aged person.
One of the scenes, that has always stood out in my memory is when she stands up in her algebra class and loudly questions the need for learning algebra because, as far as she is concerned, “nobody ever has a need to use it in their entire lives”. This of course caused the audience to burst into laughter with many heads nodding in agreement. And while many former algebra students might feel this way, I’d like to propose that an understanding of a couple of basic algebraic “tricks” can help you to prepare for CTP exam calculations in two ways. First, they can help to reduce the number of equations you need to memorize. Second, they can help when you get stuck on a calculation question because you can’t recall the required equation but by applying a little algebra, you are able to derive it from a related equation that you do recall.
For example, let’s assume that an exam question gives you information about a discounted money market instrument (e.g. T-Bill) and asks you to calculate its Discount Rate. But, you can only recall the equation for calculating its Dollar Discount, as follows:
Dollar Discount = Par Value x Discount Rate x Days/360
So, what do you do now? You can guess, but your chances of selecting the correct answer is only 25%. How about increasing you chances to 100%, by applying a little algebra. .
Here’s how it would work:
Step 1) Restructure the equation, like so,
Dollar Discount Par Value x Discount Rate x Days
______________ = ______________________________
Step 2) “Cross Multiply” (i.e. Multiply Diagonally),
Par Value x Discount Rate x Days = Dollar Discount x 360
Step 3) Isolate the Discount Rate by dividing both sides of the equation by the similar terms that are associated with Discount Rate ( in this case, the left side)
Par Value x Discount Rate x Days Discount x 360
____________________________ = _________________
Par Value x Days Par Value x Days
On the left side, the similar terms of Par Value and Days cancel out. On the right side there are no similar terms to cancel out. The result is the derived equation for Discount Rate, which is:
Discount Rate = Discount x 360 / Par Value x Days
So, while it’s true that some people might never have a use for the algebra they had to study in school, an understanding of how to apply a little bit of it can certainly help when you’re preparing to pass the CTP exam.
-George Schilling, CTP