How Money Grows
The world is full of empty promises. Advertisements tell us to buy an amazing cream because it will make us beautiful, or to buy that weird-looking contraption because it will tone our muscles and make us popular.
And here comes the Fool, with another promise. Invest money now and we'll help make you a millionaire, or at least comfortably well-off in your adulthood. Gee, that sounds even less believable than the beauty cream, doesn't it? But it's true.
If you leave your money to grow for a long time, $100 can turn into a million dollars. No, seriously. How? Through compounding.
Do you see what's happening ? Your initial bundle of $100 is growing, and the amount by which it's growing is also growing. That's compounding in action. In just eight years, you doubled your money. If you had just added 10% of $100 each time, that would have been $10 every year, and you'd have ended up with $180. But since your money was compounding, it grew faster.
If this doesn't seem magical enough for you, here's a continuation of the earlier table, showing certain years that are farther out:
Now that's magical, isn't it ? Here are a few key things to notice:
You started with just one single investment of $100. In Year 25, your wealth grew by $108! In that single year, you made more than your entire initial investment. And the following year, you made even more than that.
The world is full of empty promises. Advertisements tell us to buy an amazing cream because it will make us beautiful, or to buy that weird-looking contraption because it will tone our muscles and make us popular.
And here comes the Fool, with another promise. Invest money now and we'll help make you a millionaire, or at least comfortably well-off in your adulthood. Gee, that sounds even less believable than the beauty cream, doesn't it? But it's true.
If you leave your money to grow for a long time, $100 can turn into a million dollars. No, seriously. How? Through compounding.
How does compounding make my money grow faster?
You can make your money grow faster if you don’t spend your return. Instead, keep investing it, along with the money you started out with. This process is called compounding. It means you have more money to invest and grow. Compounding works for both guaranteed and non-guaranteed investments.
How does compounding work with a guaranteed investment ?
Let’s say you have $10,000 to invest for three years in a Guaranteed Investment Certificate (GIC). You know you’ll earn 3.4% interest. The 3.4% return goes into your GIC account once a year. In other words, it compounds annually. If you just let the interest stay there, you are reinvesting it. If you keep reinvesting, here’s what you’d make over three years:
GIC
You can make your money grow faster if you don’t spend your return. Instead, keep investing it, along with the money you started out with. This process is called compounding. It means you have more money to invest and grow. Compounding works for both guaranteed and non-guaranteed investments.
How does compounding work with a guaranteed investment ?
Let’s say you have $10,000 to invest for three years in a Guaranteed Investment Certificate (GIC). You know you’ll earn 3.4% interest. The 3.4% return goes into your GIC account once a year. In other words, it compounds annually. If you just let the interest stay there, you are reinvesting it. If you keep reinvesting, here’s what you’d make over three years:
GIC
You invest $10,000.00
End of Year 1 $10,340.00
End of Year 2 $10,691.56
End of Year 3 $11,055.07
How does compounding work with a non-guaranteed investment ?
What if you invested $10,000 in a mutual fund for three years instead? You might find it goes up 5% in the first year, but then it loses 1% the next year. In year three, it gains 7%. It also pays you income each year in the form of distributions. If you decide to reinvest your distributions into more units, here’s what you’d gain or lose each year:
Mutual Fund
You invest $10,000.00
End of Year 1 $10,500.00
End of Year 2 $10,395.00
End of Year 3 $11,122.70
Making regular payments to yourself, even in small amounts, can add up over time. The amount by which your money grows depends on the interest earned and the amount of time you leave it in the account.
End of Year 2 $10,691.56
End of Year 3 $11,055.07
How does compounding work with a non-guaranteed investment ?
What if you invested $10,000 in a mutual fund for three years instead? You might find it goes up 5% in the first year, but then it loses 1% the next year. In year three, it gains 7%. It also pays you income each year in the form of distributions. If you decide to reinvest your distributions into more units, here’s what you’d gain or lose each year:
You invest $10,000.00
End of Year 1 $10,500.00
End of Year 2 $10,395.00
End of Year 3 $11,122.70
Making regular payments to yourself, even in small amounts, can add up over time. The amount by which your money grows depends on the interest earned and the amount of time you leave it in the account.
Here's an example of your money not growing:
If you have $1,000 stashed away under your mattress for 1 year, it will still be $1,000 at the end of the year. Your mattress is not paying you interest for keeping your money.
Now let's look at interest and the power of compounding. This is how your money can grow.
When you compound interest, you earn money on the interest you leave in your account. Interest can be compounded daily, monthly, quarterly or annually. Not all savings accounts are created equal !
If you have $1,000 stashed away under your mattress for 1 year, it will still be $1,000 at the end of the year. Your mattress is not paying you interest for keeping your money.
Now let's look at interest and the power of compounding. This is how your money can grow.
When you compound interest, you earn money on the interest you leave in your account. Interest can be compounded daily, monthly, quarterly or annually. Not all savings accounts are created equal !
The Magic of Compounding
If you're not the type who enjoys math class, who delights in solving for X and figuring out how long it will take a plane to get from Los Angeles to New York if it's going 650 miles per hour, you might expect this section to be boring. It's all about numbers, after all. Give it a chance, though -- these numbers will show you how money grows and how millionaires are made.
Just how magical compounding can be depends on three factors:
1. How much money you invest
2. How much time it spends growing
3. Its rate of growth
Let's look at some examples, to see how it can work.
Compounding is when something grows over time, and the amount by which it grows is also growing. It's much easier to understand when you consider some examples.
Let's start with a simple example. We'll use 10% as our annual growth rate and start small, with $100. Let's call this Year 0, when we start with $100. One year later, in Year 1, our $100 has grown by 10%. Since 10% of 100 equals $10, we add that to our money and end the year with $110. Got that? (Note: Remember, to find out what 10% of anything equals, just multiply the number by 0.10. To find 5%, multiply by 0.05. For 25%, by 0.25.)
In Year 2, we add another 10%. But this time you don't end up with $10. Ten percent of $110 is $11. So we end Year 2 with $121 ($110 plus $11 equals $121). In Year 3, we add 10% again, or $12.10. Our new total is $133.10. Here's a table that will make it clearer :
If you're not the type who enjoys math class, who delights in solving for X and figuring out how long it will take a plane to get from Los Angeles to New York if it's going 650 miles per hour, you might expect this section to be boring. It's all about numbers, after all. Give it a chance, though -- these numbers will show you how money grows and how millionaires are made.
Just how magical compounding can be depends on three factors:
1. How much money you invest
2. How much time it spends growing
3. Its rate of growth
Let's look at some examples, to see how it can work.
Compounding is when something grows over time, and the amount by which it grows is also growing. It's much easier to understand when you consider some examples.
Let's start with a simple example. We'll use 10% as our annual growth rate and start small, with $100. Let's call this Year 0, when we start with $100. One year later, in Year 1, our $100 has grown by 10%. Since 10% of 100 equals $10, we add that to our money and end the year with $110. Got that? (Note: Remember, to find out what 10% of anything equals, just multiply the number by 0.10. To find 5%, multiply by 0.05. For 25%, by 0.25.)
In Year 2, we add another 10%. But this time you don't end up with $10. Ten percent of $110 is $11. So we end Year 2 with $121 ($110 plus $11 equals $121). In Year 3, we add 10% again, or $12.10. Our new total is $133.10. Here's a table that will make it clearer :
Year
|
Start with
|
Add 10%
|
0
|
$100
|
$10
|
1
|
$110
|
$11
|
2
|
$121
|
$12.10
|
3
|
$133.10
|
$13.31
|
4
|
$146.41
|
$14.64
|
5
|
$161.05
|
$16.11
|
6
|
$177.16
|
$17.72
|
7
|
$194.88
|
$19.49
|
8
|
$214.37
|
If this doesn't seem magical enough for you, here's a continuation of the earlier table, showing certain years that are farther out:
Year
|
Start with
|
Add 10%
|
8
|
$214.37
|
$21.44
|
10
|
$259.37
|
$25.94
|
15
|
$417.72
|
$41.77
|
20
|
$672.75
|
$67.28
|
25
|
$1,083.47
|
$108.35
|
30
|
$1,744.94
|
$174.49
|
35
|
$2,810.24
|
$281.02
|
40
|
$4,525.93
|
$452.59
|
45
|
$7,289.05
|
$728.90
|
50
|
$11,739.09
|
$1,173.91
|
You started with just one single investment of $100. In Year 25, your wealth grew by $108! In that single year, you made more than your entire initial investment. And the following year, you made even more than that.
Notice how large the total gets. You started with $100, but in 50 years, that's become almost $12,000. (A stickler might point out that thanks to inflation you won't be able to buy as much stuff in 50 years with that $12,000 as you could buy with $12,000 today. But then, today you just have that $100. You're still coming out way ahead.)
Notice that the longer you let your money compound, the more massive each year's growth becomes. In the first years, you just added $10 or $20 or $30 per year. But after 25 years, you're adding hundreds each year. Compounding gets more powerful the longer it's left to work.
The Rule of 72: A quick way to estimate the effects of compounding !
The Rule of 72: A quick way to estimate the effects of compounding !
This is a quick, rough way to estimate how long it will take you to double your money with compound interest. Simply divide the number 72 by the interest rate you earn each year, and that’s the number of years you’ll need. The Rule of 72 is not exact, but it works pretty well, as long as the interest rate is less than 20%.
Example: Let’s say you have $5,000 invested at 6% per year. You divide 72 by 6 and get 12. By the Rule of 72, you’ll double your money in about 12 years if you let your interest compound.
Compound Interest Exercise:
$1,000 @ 5% compounded annually earns $50 of interest at the end of one year. (You made more than if you kept it under your mattress!)
If you deposit $1,000 in an account that has daily compounding, at the end of the first day you would have $1,000.14. ($1,000 @ 5% divided by 365 days)
The next day, the interest is calculated based on the entire amount of your original deposit of $1,000 PLUS the previously earned interest -- $1,000.14 rather than just $1,000.
By the end of one year you would have $1,051.27. The extra $1.27 does not seem like much at this point. However, the table below shows the difference it makes over time.
This table uses the same $1,000 to show how your money grows faster the more often interest is compounded and the longer it stays in the account. The 14 cents adds up over time!
The table below shows that even small amounts of savings add up. Look what happens when you save just $1 a day.
At the end of year 1, you would make an extra $9 compounding interest. The real power of compounding shows at the end of 30 years, you would make an extra $14,465!
The table below shows what happens to your money when you save just $5 a day. Look at the difference when your money is invested in an account that compounds interest daily.
$1,000 @ 5% compounded annually earns $50 of interest at the end of one year. (You made more than if you kept it under your mattress!)
If you deposit $1,000 in an account that has daily compounding, at the end of the first day you would have $1,000.14. ($1,000 @ 5% divided by 365 days)
The next day, the interest is calculated based on the entire amount of your original deposit of $1,000 PLUS the previously earned interest -- $1,000.14 rather than just $1,000.
By the end of one year you would have $1,051.27. The extra $1.27 does not seem like much at this point. However, the table below shows the difference it makes over time.
Interest
Type
|
5 Years
|
10 Years
|
No
Interest
|
$1,000
|
$1,000
|
Annual
Compounding at 5%
|
$1,276
|
$1,629
|
Monthly
Compounding at 5%
|
$1,283
|
$1,647
|
Daily
Compounding at 5%
|
$1,284
|
$1,649
|
The table below shows that even small amounts of savings add up. Look what happens when you save just $1 a day.
Years
|
No
Interest
|
5% Daily
Compounding |
Year 1
|
$365
|
$374
|
Year 5
|
$1,825
|
$2,073
|
Year 10
|
$3,650
|
$4,735
|
Year 30
|
$10,950
|
$25,415
|
The table below shows what happens to your money when you save just $5 a day. Look at the difference when your money is invested in an account that compounds interest daily.
Years
|
No
Interest
|
5% Daily
Compounding |
Years 1
|
$1,825
|
$1,871
|
Years 5
|
$9,125
|
$10,366
|
Years 10
|
$18,250
|
$23,677
|
Years 30
|
$54,750
|
$127,077
|
The table shows a difference of only $46 at the end of the first year. However, compounding daily after 30 years show a difference of $72,327!
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