I’m going back to college, college, college…

Growing up in grade school I always felt like we were learning a bunch of crap that I would never use in real life. My teachers told me to learn foundational concepts in the physical sciences, mathematics, and social studies, while were great to learn, had very little life application except in dinner table conversations or if you wanted to teach these subjects. Even in college, while half of my education provided the necessary training for my first job the other half was an expensive donation to the higher educational system. Colleges and universities promised a well-rounded education. But, personally if they would have only focused on the courses I needed for my degree and gave me credit for all of the parties and social scenes that came with the college experience that would have provided more than enough for a more well-rounded education.

However, after starting on my journey to go back to school I now look at the educational system or process a bit different. I have been taking continuing education classes ever since I left school the first time. But, now I am officially working towards another degree, which is a different sort of feel at this juncture.

I just finished up summer school by taking College Algebra and you know what, it was not too bad! At the suggestion of a math mentor of mine I have been instructed to start at the foundation of mathematics again in order to better grasp the more advanced concepts. Even a buddy of mine who just completed his masters degree in civil engineering cum laude indicated that math instructors expect you to have mastered algebra when they begin the teach derivatives, integrals, and even linear algebra.

How much do I need in retirement?

In a section of my algebra class we covered “Applying Exponents and Logarithms” and it reminded me of my last blog where I lamented about how important financial planning was in our personal financial lives. Then I stumbled upon an old article from CNBC that provided a lot of rhetoric about the age-old question, “how much money does one need in retirement?” Obviously, it depends…but, I thought being the geek that I am I would take it a step further.

In algebra class I re-learned about the Future Value Sum Calculation, which is an algebraic equation that takes in parameters and calculates how much money you have today and what it will be worth tomorrow based on certain conditions. The equation or function is as follows.

A = P(1 + r/m)^tm

where:

A = Future Value

P = Present Value

r = interest rate (in decimal form)

m = number of compounded periods (quarterly, annually, etc…)

t = number of years

Now, this function does not consider continuous contributions. But, we will get to that in a second.  Let’s say for example that I am 28 years old and I believe that I need $2.5 million dollars in today’s dollars in my 401(K) when I retire at the tender age of 59 1/2, which is the minimum age you can withdraw your money without a 10% penalty tax for early withdrawal from the IRS. Also, assume that I contributed the federal limits of $18,000 per year and amassed about $100,000 even. The question is what interest rate would I need to average as a return on my investments, compounded monthly, in order to reach this goal? Hmmm…how do we solve this equation? Well, I am glad that you asked. Let’s plug the values into the equation first.

(plug in variables and known values into the equation)

(Note, we are solving for “r” or the “interest rate”)

1.)  2,500,000 = 100,000(1 + r/12)^(34)(12)

(Divide both sides by 100,000)

(Multiply number of years by number of compounding periods)

2.)  25 = (1 + r/12)^(408)

(Take 408th root of both sides)

3.)  408√25 = 1 + r/12

(Subtract both sides by 1)

4.)  408√25 – 1 = r/12

(Multiply both sides by 12)

5.)  r = (408√25 – 1) * 12

(Calculate the value)

6.)  r = 0.0950472584

(Multiple by 100 in order to turn the value into a percentage)

7.)  r = 9.5%

So, what is all of this math for again?

As a result, we need a 9.5% return on $100,000 in order to meet our financial goal in 34 years to have $2.5 millions. Believe it or not, you could accomplish this by investing in a Vanguard Healthcare Fund that continues to make historic returns due to the GDP growth in the healthcare sector.

See, our high school teachers were right! There is real application of foundational topics that we have use of in our daily lives.  In the next blog we will write a little python code, which I am also learning at the moment.  We will apply some of these financial calculations in simple python applications including continuous investment contributions on a future value sum calculation.  In the meantime, I hope you enjoyed this blog entry. Know your MATH!

 

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