52 Week Money Challenge Mathematics

The 52 Week Money Challenge incorporates a rather simple mathematical formula of Arithmetic Progression or Arithmetic Sequence. For those who don’t like mathematics, you might not agree with the notion. But at least we get to have one simple application with math. I oftentimes wonder when I was little where I could apply this sequencing notation. Alas, it has found its niche to savings.

Note: Mathematics ahead!

The Arithmetic Progression or Arithmetic Sequence is a sequence that has a constant difference between terms. We have the first term, the common difference and the number of terms.

Let us equate the three items with variables. Let us set the first term as a, the common difference as d and the number of terms as n.

The explicit formula is

an = a1 + (n – 1) d

In the case of the 52 Week Money Challenge, our first term would be 50, our common difference is 50 and the number of terms 52. The 52 indicates the number of weeks in a year.

So for instance, if we have 50, 100, 150, 200 this has a1=50, d=4, and n=4

So we apply these values to the explicit formula we can derive this:

an = 501 + (4 – 1) 50

The sum of the members of the finite arithmetic progressions is then called the arithmetic series. For instance with regards to the 52 Week Money Challenge we consider the sum of 50 + 100 + 150 … + 2600.

The sum can be computed by taking the number n of terms being added. The challenge implies 52 in this case. Then we multiply the sum of the first and the last number in the progression. In this challenge we have 50 + 2600. After taking the sum we then divide it by 2.

n (a1 + an)
In the case of the 52 week money challenge, this gives us the following equation

52 (50 + 2600)

The answer would be 68,900. Hence, by the end of the 52 weeks, you could indeed save up that much amount.

If you want to do the computation monthly, you can add in 50 + 100 + 150 + … +2600. It would still yield a total of 68,900.

So you gotta love Math! 

P.S. To those doing the 52 Week Money Challenge and 52 Week Money Challenge Version 2, it is Week 12 already! Did you deposit the next amount yet?

P.P.S Want to know more about investing, savings, stock market and more, check out my reference here. You can download free ebooks and resources too.