More tips that will turn you in to a business math star.
In the last article, we kicked off our two-part business math boot camp with tips that will help you perform mental math quickly and confidently, understand and work with percentages, and use the fact that you are pretty to solve simple interest problems. In today’s article, we’re going to finish up our boot camp with 3 more tips to help you continue your metamorphosis into a business math superstar.
Tip 1: Get to Know the Simple Interest Formula...Even Better
The final tip in the first part of this business math series was about getting to know the simple interest formula. As you’ll recall, all you have to remember about the simple interest formula are the three words: “I am pretty.” In other words, I = P x r x t…which says that the interest you make on an investment, or that you owe on a loan, is equal to the principal amount invested or borrowed, times the interest rate per year, times the number of years the money is invested or borrowed.
But what if that time period isn’t given in years? What if it’s given in months, or days, or even hours? For example, imagine that you’ve put $1000 into an investment earning 5% interest per year, but that you only intend to let it accrue interest for 9 months. Can you still use the simple interest formula to figure out how much interest you’ll earn?
Absolutely! The quick and dirty tip for a case like this is to write the amount of time as a fraction relative to the length of a year. Since there are 12 months in a year, we can calculate the interest earned on your 9 month investment using the formula:
I = $1000 x 0.05 x (9 / 12) = $37.50
Or if the investment had been for 25 days instead, we would use the formula:
I = $1000 x 0.05 x (25 / 365) = $3.42
To sum up: If the interest rate is given as a percentage per year, the time can be either a whole or a fractional number of years.
Tip 2: Use the Rule of 72 to Make Compound Interest Easy
Interest isn’t always so simple. In fact, for many types of investments, the simple interest formula isn’t even the right formula. For investments like CDs, stocks, bonds, and for debts like credit cards, interest compounds every year. What does that mean? It means that the interest earned or owed each year itself earns more interest or becomes more interest owed the next year.
In other words, if you invest $100 at a 10% interest rate for a year, you will earn $10 of interest at the end of the year. But if that investment instead compounds for 2 years, and you keep all the interest earned from the first year in the account, then in the second year you’ll be earning 10% interest not on $100, but on $100 + $10 = $110. And the interest keeps on compounding like this year after year.
If you need to know exactly how to calculate how money grows in a compound interest earning investment, you’ll want to use the compound interest formula.
But if you just need to come up with a pretty good estimate of how long it’ll take your money to double in an account like this, all you need to know is the rule of 72. The quick and dirty tip is to divide the number 72 by the interest rate, and the number you get will be the approximate doubling time. So a 10% interest rate gives a doubling time of about 72 / 10 = 7.2 years, a 5% interest rate gives a doubling time of about 72 / 5 = 14.4 years, and so on. The rule of 72 is great for those times when you need to come up with quick and easy estimates in your head.
Tip 3: Understand Mean and Median Values
For the final tip in our business math boot camp, let’s change gears and talk a bit about average values. In the business world—and in the rest of the world too, for that matter—you’ll hear terms like “average,” “mean,” and “median” thrown around all over the place. And it’s important that you know the differences between them. So what are they?
The first thing you should know is that the goal of finding an average value is to come up with a single number that represents the typical value of a group of numbers. The second thing you should know is that the mean and median are both averages—they’re just two different methods for coming up with a typical representative number.
When people talk about finding “the average,” they’re usually referring to the mean. You find the mean by adding up all the numbers in a group and then dividing the result by the number of numbers you added up. To find the median, all you have to do is write the numbers in the group from smallest to largest, and then select the number right in the middle. Learn more in my earlier articles about how to calculate and interpret the mean and median.
But how can you keep these two terms straight in your head? The quick and dirty tip is to remember that the word “median” has the same number of letters as the word “middle,” and the median is always the middle number. So the median is the number in the middle, and the mean is the other one.
Number of the Week
Before we finish up, it’s time for this week’s featured number selected from the various numbers of the day posted to the Math Dude’s Facebook page and to QDT’s new blog, The Quick and Dirty. This week’s number is 530 trillion. Why? Because that’s the approximate number of Olympic-sized swimming pools you’d need to hold all the water in all of Earth’s oceans. To give you a bit of perspective on just how enormous this number is, there are roughly 5 Olympic-sized swimming pools of water on Earth for every single cell in your body. That’s a lot of water!
Okay, that’s all for today. Remember to become a fan of the Math Dude on Facebook where you’ll find a new number of the day and math puzzle posted each and every weekday. And if you’re on Twitter, please follow me there too. Finally, if you have math questions, feel free to send them my way via Facebook, Twitter, or by email at email@example.com.
Also, as I mentioned in the first part of this series, I’ve put together a new hour-long audiobook called The Math Dude’s 5 Tips to Mastering Mental Math that’ll walk you step-by-step through 5 of the best mental math secrets and get you up and running quickly. It’s available for less than $1 from Amazon, Audible, and iTunes...so please check it out!
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
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