Good topic as any to begin my blog…
Okay, so you are probably saying to yourself, “Uh, who cares about my retirement age, my financial advisor already figured everything out for me” or something along those lines. Well that’s fantastic actually, I hope everyone has a savings and investment plan for the future. But the reason for writing this article is to get you thinking in terms of math.
For example, often times in government an employee knows when he is eligible to retire and possibly draw a pension not by the number of years worked but by a rule, like the rule of 80. This means that your age and the number of years worked have to total 80. You might say, that is easy to figure out. Which you would be right in saying so. So can you tell me at what age a 32, 24 and 40 year old will be eligible for retirement and and how many years they will have worked given the rule of 80? Also, each employee has been working 2, 0 and 4 years respectively. Oh, one last thing, can you calculate the answer in under 2 minutes?
… 2 minutes later …
If you were able to figure it out in two minutes great. If not, here is a way to do it withtout doing so much backward and forward, division and subtraction.
First of all let’s write our first problem out.
There is a 32 year old employee. He has been there 2 years. Therefore he started at 30. Let us write the equation now.
Starting Age Yrs. + (2 * Service Years) = 80
Starting Age Yrs. = x
Service Years = y
Employee 1: Currently 32, started 2 years ago at age 30.
1.) 30 + 2y = 80 [Write down the equation plug in known values]
2.) 30 + 2y – 30 = 80 -30 [Simplify equation by subtracting 30 from both sides]
3.) 2y = 50
4.) 2y / 2 = 50 / 2 [Divide both sides by 2]
5.) y = 25 [Service Years = y = 25]
So for the 32 year, who started at age 30, they will have to work for 25 years in order to reach the rule of 80. He will be 55 years old. How about the other two? Just use the same formula, plug in their starting age and you will get the answers.
Really quickly though, in our equation x + 2y = 80, why do we multiply y by 2? The answer is simple, we know that y stands for service years and x stands for starting age but we need to take into account that the employee will also age by the number of years that he will work, thus adding to his age. The first employee will not be 30 forever. Another way of looking at is:
Starting Age Years + Service Years + Service Years (Aged) = 80
Here you will have x + y + y = 80 or x + 2y = 80.
Simple problem right? Well it can be more difficult than it should be if we don’t take the time to think mathematically.
By the way, check your answers: 24 year old, needs to work 28 years. He’ll be able to retire when he is 52 (24 + 28) years old. The 40 year old can retire when he is 58 (36 + 22).