I went to a cat show this weekend. If you have never been I recommend it. I saw some fantastic cats. If you are used to the domestic short hair or long hair, some of these cats might look unusual. They did to me!
“Oh no!” You might be groaning to yourself. “What is she going on about now.” Actually, I’m going to go on about compound interest.
Bear with me. This won’t take long to read and you might save yourself a bunch of money (and I included photos to keep it fascinating). As a bonus, if you read to the very end I show you how to get $15,000 in free money! Wow. So, read on my friends.
If you use a credit card, have a mortgage, or are otherwise involved with borrowing or investing money, then you should have an understanding of compound interest. It’s how the rich get richer and the poor go broke.
Here is how it works: When you borrow money you pay it back with interest. Interest is simply the amount of money (usually a % of the total loan) that the lender charges you for allowing you to borrow that money. Or, in the case of an investment, it is what the institution pays you for letting them use the money you have invested (deposited) with them.
When the interest is compounded it means that the interest you owe each month (or quarter or year, depending on how often it is compounded) is added to the total you owe. This means you are paying interest on the interest.
There are set formulas to determine the math and different companies do things a little differently. Often loans are arranged so the monthly payments are all the same. In the case of a mortgage it is usually set up so you pay more of the the interest in the beginning and only after the bank has gotten a good portion of the interest do you start paying the the principle of the loan. In each case, however you end up doling it out, the interest will accumulate, that is, it will compound.
For example, say you have $1000 in a bank account earning 5% interest each year (unlikely, but the math is a lot easier than 1.46%). If it is a flat 5% rate, at the end of the year you will have $1050. Pretty straightforward.
If the interest is compounded monthly then it gets more complicated – but if you are the investor it is well worth it.
Using the same example of $1000 over a year at 5%, in the first month you get 1/12 (one month’s worth) of the yearly interest. That is $50 per year, divided by 12 months, or $4.17.
So, $4.17 is added to your balance. Now, in your second month you have 1004.17 in your account. Again you get 1/12 of the yearly interest. But now that is 5% of $1004.17 so your monthly interest is now $4.18. The third month you are getting paid 5% of 1004.18, so your 4th month you will be getting interest on a bit more than the third month. By the end of your first year you will have earned $1051.20.
Big deal, you might be thinking grumpily to yourself. I have to read all this for a measly $1.20 a year.
Yes, but not so fast.
Now lets look at your credit card. A credit card is simply an easy way to borrow money. You hand over the plastic, some bank somewhere coughs up the payment and you walk happily away clutching your widget under your arm. Unfortunately, at some point you need to pay the piper/banker.
Say you owe $1000 on your card at 20% interest (much more realistic than the 5% at the bank). First you need to know if that 20% is the interest rate alone, or the APR (Annual Percentage Rate). The APR includes all that compounding, so it is a more realistic number. Credit cards have to tell you the APR. Look for it on your card and see what you are paying.
If you have a flat 20% rate (you don’t), by the end of the first year you will owe $1200 ($200 = 20% of $1000). If your credit company compounds the interest monthly (likely) then it works the same as it did with your bank account, only less happily for your financial well being.
The first month you will owe $16.67 in interest ($200 interest per year divided by 12 months). This gets added to your balance. You now owe 1016.67 total. The next month you will owe a total of $1084.72, because of the interest added to your original balance. By the end of the year you will owe $1219.39, for an APR of 21.94%. So, by compounding your interest, 20% turns into 21.94%.
In that scenario, for ever $78.06 you spend you are handing over $100. That $21.94 of each $100 is what you pay for the privilege of borrowing the money (ie using your credit card). People with low incomes or a bad credit record end up paying higher interest rates. It becomes harder to borrow and the loans get harder to pay off. This is a recipe for going broke.
On the other hand, if you can pay off your card every month you are paying $100 for every $100 you borrow. In that case the annual fee (if there is one) is the only money you are actually paying the credit card company. Now that is a good deal. It doesn’t get much better than a 0% loan.
If you can’t pay off your credit card it can quickly add up. That is because credit card rates are so high and often if you are late on a payment they go even higher.
But even at low rates compound interest adds up, all it takes is time. This is how the rich get richer.
Say you have $100,000 lying around that you invest at 3.92% APR. In 30 years you will have $170,213. You will have “earned” $70,213. Those numbers are actually for a mortgage, but it works the same way whether you are borrowing or investing (although the difference to your purse is considerable). So, if you flip to being the borrower, then in this example, the bank will have charged you $70,213 for your mortgage. Remember, that is at 3.92% while credit cards can easily be 15-30%.
But here is the promising part.
Say you can put away $50 each month starting when you are 30. In those same 30 years, at the same 3.92% you will save $33,204.28. Not bad, considering that the amount you actually invested was $18,000 ($50/month = $600/year x 30 years = $18,000). That is the real magic of compound interest. It grows faster and faster over time as your money snowballs. It is much better for your finances if you invest the money rather than borrow it!
So, I recommend you pay off your loans and start putting money away.
That my friends, is my lecture for today.
Enjoy the day,
Did you know that shape shifting lizards are living among us? Many politicians, including Hilary Clinton, George Bush and Queen Elizabeth, are actually blood-sucking aliens. (This invasion was brought to light in the 1990’s by David Icke.)
Did you know that climate change is a hoax perpetuated by the Chinese as a way of hurting the US. (Our president said so.)
Actually, I know both Icke and Trump are wrong, but how do I know? When I say I know something, what do I mean? In this day of alternative facts and outright lying how do we know what is true / real?
That is the question I’m going to explore in great and philosophical depth. I hope you stick around for it.
I know the sun is hot.
I know Clinton is not an alien lizard.
I know that the earth is warming.
I know 2 + 2 = 4.
I know Beta loves me.
These are different types of knowledge.
I know the sun is hot because when I sit in the sun I get warm and if I stay out too long I get a sunburn.
I know Clinton isn’t a lizard because I’m a reasonable person (at least, I like to think so).
I know climate change is real because the majority of climate scientists agree it is and show evidence ranging from the loss of Antarctic ice sheets to steadily increasing average global temperatures.
I know 2 + 2= 4 because my teacher told me so and every time I add 2 + 2 it = 4/
I know Beta loves me because she wags and wiggles from head to tail while giving high pitched yelps of joy when she sees me (and isn’t that great for the ego).
Now let’s look at each example a bit more closely, starting with how things can go wrong and what we can do to prevent that.
Our senses give us massive amounts of information each day. We take that experience and base knowledge on it. However, our senses can be wrong, or our interpretation might be off.
If I go outside on a day like today, when the sun is shining and it’s a beautiful -10 ℉, I might assume the sun is making it cold out. If I never experienced the sun that is just as reasonable as thinking the sun is making it hot when it 95℉. Fortunately, I go outside in all weather, and, yes, the sun makes it hotter (I recommend a moonlit walk when it is below zero. Beautiful. Brisk.) Repetition provides confirmation that the sun is hot.
The second example, well, the idea of shape-shifting aliens (reptilians is the official term) is ridiculous. But, then again, it’s also ridiculous to imagine an earthling who can shape shift and change color to match its surroundings – like an octopus.
Hmm, being a ridiculous idea isn’t enough. However, another reason I just can’t believe in aliens (much as I would like to) is that all the evidence for their existence is hearsay from questionable sources. Meanwhile, the evidence against their existence is pretty overwhelming.
1) No person has ever turned into a lizard (although over hundreds of millions of years it could be said that lizards turned into people, if you count the first thing that crawled from the ocean as a lizard).
2) No aliens have ever been seen (although there is hope for finding microbes on Titan).
3) While politicians change political shape with some regularity, you would think a doctor would have noticed if any of the above was a lizard in disguise.
On the other hand, we have massive amounts of evidence that climate change is happening. Numerous studies in a wide variety of fields have shown both cause and effect. Studies have been repeated by other scientists with similar results, leading to a global consensus among the scientific mainstream. If it was just one or two scientists, well, they could be wrong, but in this case, unless there is a major conspiracy by science and the media in general…. (an idea which, frankly, is as ridiculous as the shape shifting aliens).
Evidence against climate change is often put forward by politicians who clearly have no understanding of the issues (confusing climate and weather for instance). The scientists who argue against global warming have been refuted by their peers. That’s enough for me to trust my knowledge that climate change is real.
Third, I know 2+2=4 because it is understood. And it works. I can take 2 pebbles and then add two more and I will have 4 pebbles. I can do the same thing with muffins or kittens or houses. In fact, I can do it with everything, including abstractions like numbers. “Knowing” in math is a bit different from other knowledge because of the strictures of mathematical logic. Since I don’t know much more than 2 + 2 = 4, I’ll leave math aside for now.
Finally, there is my girl Beta. Dogs wag and wiggle when happy. Beta wags and wiggles when she sees me therefore Beta is happy to see me. Besides, what else could she be saying? Actually, since we can’t get into her head I can’t ever really know what she is thinking or feeling, so I have to go with how she has behaved in the past, how other dogs behave and what dog trainers have told me.
In case you are getting lost, we have now looked at several different ways of knowing things, each of which has its drawbacks. Our senses can be wrong, our sources can be wrong, our understanding can be wrong. With so much information at our fingertips we need to be careful.
The moral of the story is that it’s not safe to take things on face value. Rather, if you want to have confirmation, look at your ideas different ways. Think about the source, compare with your own experience and also look at what the science says. Despite it’s reputation, science can and does give us huge amounts of knowledge about the world in which we live.
We are heading into some cold weather here in the frozen North-lands. The rumor is that it might not get above zero F. this week. Last week was warm(er) and sunny and the transition from warm to cold has been beautiful.
I took a walk in -10 weather this morning and the sun was sparkling on all the ice formed earlier, so I took some photos.
I hope you enjoy them.
Dec 27, 2017
If you enjoyed this post you might like these as well:
Now this is quite a large dictionary, so the publishing company decides to break it into 26 volumes, one for each letter. Since the company is concerned about ink, they decide to also drop the first letter in each volume, since everyone knows that in the A volume each entry starts with the letter A, etc. So, their first volume looks like this:
But wait, dropping the first A does nothing. No, it does more than nothing, it means the first volume now contains the entire dictionary. How can subtracting an infinite number of letters not change anything? Like I said infinity is weird.
Another quick example: There are the same number of even numbers as there are odd and even. You can make a one to one correspondence this way:
1 2 3 4 5 6 7….
2 4 6 8 10 12 14…
It seems like cheating, but by the same token, because of infinity .99999… is equal to (not close to, but the same as) 1.
now multiply both sides by 10
now subtract the first equation from the second
10X=9.9999999… – X=0.99999999… 9X=9
the infinite progression of .999999 cancels out, divide each side by 9
and you are left with
X=1 so plug X into your original equation and
I’d like to introduce you to a cloud. It’s called Asperitas and it’s a beautiful thing (although it can accompany some ferocious weather).
It was recently recognized as a supplemental feature of the species stratiformus by the World Meteorological Organization on March 23rd 2017 (World Meteorological Day).
Clouds are complicated things as anyone who has ever experienced weather knows. Air is full of water vapor and when that vapor cools it condenses and forms clouds. The water vapor consists of tiny droplets so light they blow around rather than falling, so precipitation only occurs when the vapor freezes into clumps of water droplets that are heavy enough to fall to the earth.
Clouds are broken into 3 main classes based on their place in the atmosphere (high, middle or low). Within those classes are 10 genera, 14 species and 9 varieties. Beyond that are a few special clouds with their own descriptions, for a total of around 100 different descriptions.
High clouds are those with a base roughly 6-18 k (3-11 miles) above sea level. There are three genera for high clouds:
cirrus, cirrocumulus and cirrostratus.
Middle clouds are from 2-4 k (1.25-2.5 miles) above sea level. Again there are three genera:
altostratus, nimbostratus, and altocumulus.
Low Clouds are 0-2k (0-1.25 miles) above sea level and the genera are:
cumulus, cumulonimbus, stratocumulus, and stratus.
As you probably noticed, several words show up often. Those are form descriptors.
Cumulus clouds are heaped, puffy clouds.
Stratus are sheet clouds, horizontal rather than piling up.
Cirrus clouds are wispy and fibrous.
nimbus means rain bearing clouds
and alto is simply mid-level.
Then within each of these general forms the classifications become more and more specific. The 14 cloud species describe the shape and the form of the cloud. Species include include wonderful things like “uncinus” meaning shaped like a hook or comma, and spissatus which is “dense enough to appear grey near the sun,” cavum refers to a cloud with a hole in the middle.
Asperitas is the newest addition to the family. As a member of the species stratiformus we know it is stratus therefore a sheet cloud, not a puffy or fibrous one. However, stratiformus can be altocumulous or stratocumulous, so it becomes more complicated. Now we also know that asperias can be at middle or low levels in the atmospere and that it isn’t simply a sheet but also has puffy aspects. This sounds like a confused cloud. It looks like one too. The name fits perfectly!
So, now that you have been introduced – ever so briefly – to clouds take a peek outside and see if you can tell what’s up.
You can get your own cloud chart here or see details of cloud classification here.
It was the closing of the day
when the geese filled the sky,
honking hollow echoes of sound.
Wings curved, close, over the water.
When the geese filled the sky
their reflection held the sunlight, in
wings, curved close over the water.
Landing in sunset ripples on the pond
their reflection held the sunlight in,
floating now. The geese circled once,
landing in sunset ripples on the pond
for the light was fading.
Floating now the geese circled once,
settling, preening, then quiet,
for the light was fading.
The ripples smooth like feathers
settling. Preening, then quiet
the sun entered the pond,
the ripples smooth, like feathers,
covering the dark water.
The sun entered the pond
and night filled the sky
covering the dark water.
It was the closing of the day.
STILL LIFE WITH PAINTING (BLACK CAT)
The black cat licks her white paws
with her pink tongue. Her ears
are dark points. Around her the room
shifts and frets. Her whiskers nod
down and back. Her pink tongue traces
a foot. She is night
with light edges. She licks
her paw and wipes each keen ear.
Her task complete,
she tucks nose to tail and folds
herself into a warm spot
on the cushion. Her paws are hidden.
She is a pool of darkness, like the beginning,
like before the beginning, she is
The TV flickers its dull light,
a newspaper stirs and rattles. The red
painting swirls from the wall
and flies to the floor. She lies
in the center of the chair sleeping,
like a cat sleeping, in the center
of a chair.
Breathing sweet, clean, air is one of the simple pleasures of a walk in the woods. The air always seems fresher than that beyond the forest.
There is a reason for that. You are breathing brand new oxygen produced by the very trees surrounding you. How does this happen? It happens through a truly miraculous process known as photosynthesis.
What is photosynthesis?
Photosynthesis is the means by which trees and other plants turn sunlight into food. It’s a process that all green plants, as well as algae and some bacteria, use for their growth. Since I love trees I will concentrate here on the photosynthesis used by trees around the world.
How does photosynthesis work?
In the most common form of photosynthesis, the chlorophyll in the tree’s foliage captures light energy in the form of photons. Through a series of of biochemical transformations, the tree uses that energy to turn carbon dioxide and water into simple sugars which fuel the tree’s growth.
The photons provide the energy needed for water and carbon dioxide (collected mainly in the tree’s leaves and roots) to be transformed into other molecules. Through a series of steps the carbon dioxide and water are changed into simple sugars, leaving oxygen as a waste product.
The general formula looks like this:
6 CO2 + 12 H20 + photons = C6H12O6 + 6 O2
In English that is:
6 carbon dioxide molecules plus 12 water molecules plus light energy leads to 1 glucose molecule and 6 oxygen molecules. (Doesn’t seem like much but multiply by trillions of molecules and it starts to add up.)
What is chlorophyll?
Chlorophyll is a molecule found in green plants. In fact, it is what gives the plants that green color. This essential molecule is what allows photosynthesis to happen, by combining with other molecules to transform light and carbon dioxide into oxygen and other byproducts.
The tree then transforms glucose (sugar) into the biochemical fuels needed to grow and reproduce. At the same time, the process releases excess oxygen into the air through pores in the tree’s leaves.
What is a photon?
Without getting into quantum
mechanics (!) you can think of a
photon as a sort of bundle (a quanta)
of light, an individual “thing” that
smacks into the tree as sunlight. Just
don’t tell your physics friends that I
described it that way, since photons
don’t actually have any mass.
A more sophisticated answer to the
question of what a photon is can be
found at http://www.wisegeek.org/what-is-aphoton.htm.
Why Should We Care?
To be selfish about it, one reason is because we can’t live without it.
More specifically, photosynthesis plays three important roles.
1) It feeds the tree. Without it we couldn’t walk in the woods because there would be no woods.
2) It “fixes” carbon, meaning it takes carbon dioxide, which is a greenhouse gas and puts the carbon into a solid form (such as in the glucose or other sugar produced), thereby reducing the amount of CO2 in the air.
3) It releases oxygen into the air as a waste product. In essence, trees and other plants “inhale” CO2 and “exhale” oxygen, while we humans and other animals do the opposite.
Green plants are essential in
helping stabilize the environment
by taking up CO2. Unfortunately,
we humans are presently
producing far more CO2 than
plants can take up. But without
trees doing their part we would be
in far worse shape than we are
So plant a tree today and then pat yourself on the back for taking a step towards making our planet a better place.
Next time you’re in the woods think about all the trees “breathing” around you and remember that without them we wouldn’t have the oxygen we need to live.
Poison Ivy loves CO2. You may notice it growing
next to the road. It uses the exhaust from the
traffic to help grow to truly prodigious sizes (see
bush to right).
That alone should make you think twice about the
amount of excess CO2 we produce, especially
here in the USA.