The IntMath Newsletter - 1st Mar 2008
By Murray Bourne, 01 Mar 2008
In this Newsletter
1. Real life math - the power of compounding
2. Fortnightly math tips - Negative numbers
3. From the math blog
Welcome to the first fortnightly IntMath Newsletter. The monthly letters were getting very long and many readers requested shorter, but more frequent letters. I'm happy to oblige ^_^
This newsletter goes out to students, instructors and interested people in 89 different countries. A warm welcome to every one of you!
1. Real life math - the Power of Compounding
Abe and Ben are twin brothers but they have very different approaches to life. Abe thinks ahead, but Ben lives for the moment.
Abe and Ben got their first jobs when they were 20.
Abe saved $1000 per year in a term deposit earning 8% per year until he was 30. Then he got married and found he could not save any more money, but he kept his term deposit going. He worked out that he would have $67,500 when he retired at 60. In summary, he saved for 10 years and then let the money grow in the term deposit for 30 years.
On the other hand, Ben didn't start saving at 20. He kept putting it off and having a good time. Finally he was told that if he wanted to retire with the same amount as Abe, he would have to start saving $1000 per year RIGHT NOW until he retired.
It turned out that Ben was 36 when he had to start saving and he would need to save $1000 per year for the next 24 years to catch up with Abe's $67,500 by retirement.
That's more than twice as long as Abe saved for.
And that, folks, is the power of compounding. If you are saving, then compound interest - and time - are your best friends. If you start saving early, there is much less pain. But if you are a slave to your credit card, then compounding - and time - are your biggest nightmares. Your debt just continues to grow.
I guess you have heard of the "credit crunch" in the US right now? There are many people who are now wishing that they had understood compound interest a whole lot better. Their housing loans are in a big mess. You don't have to be one of these people in the future, since knowledge is power.
You can learn about interest, credit cards, borrowing for a home and lots of other really important math at...
There are some online calculators in that chapter to help you figure out savings and loans payments. It's interesting mathematics because it involves exponential growth, geometric series - and everyone's future.
They don't spend enough time on this real life math in schools...
Rule of 72: There is a really easy way to find out how long it will take to double your money - without a calculator! It's called Rule of 72 and it works like this.
If your bank is paying 10% per year, it will take about 7.2 years to double your money (because 10 times 7.2 = 72).
If you can get 6% per year, you need to wait 12 years to double your money (6 x 12 = 72).
Pretty easy, huh? And very good to know. See more examples at Rule of 72.
2. This month’s math tip - Negative numbers
Many math students (even the 'good' ones) mess up with negative numbers occasionally. And if you are shaky with number facts, then your understanding of algebra is also going to suffer.
Here's some quick reminders on stuff where things go wrong.
Subtracting a negative number: For example, 5 − −2
Here, we just add positive 2.
So 5 − −2 = 5 + 2 = 7
In math talk, we say "when subtracting an integer, add its opposite".
The opposite of an integer means the number on the opposite side of zero. In the case of -2 (which is on the left side of zero), the opposite is +2 (which is on the right side of zero). So we added +2.
Multiplying negative numbers: For example, 7 × −3
When multiplying integers, the thing to remember is:
- If the signs are the same, the final answer will be positive.
- If the signs are different, the final answer will be negative.
In our example, 7 and -3 have opposite signs, so our final answer will be negative. So 7 × −3 = -21
Another example: −6 × −5
This time, our signs are the same, so our answer will be positive. So −6 × −5 = 30.
Division of negative numbers works just the same as multiplication. Same signs, positive answer; different signs, negative answer.
For more examples on negative numbers, see Integers.
3. From the math blog
1) Friday math movie - Powers of 10
This movie is a great demonstration of powers of 10. You go for a journey out in space, and then into the atom.
2) Water from the air using windmills
An Australian invention shows great promise in extracting water from the air using an efficient windmill and a condenser based on the African stenocara beetle.
3) Laughing scale
Kansai University researchers have developed a "laughing scale", using the "aH" unit.
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