Compound Interest – Napkin Finance

“The most powerful force in the universe is compound interest.”

-Albert Einstein

The Magic of Compounding

Compound interest refers to interest earned on an initial investment as well on the interest already earned.

While simple interest is calculated once for the entire period of a loan, compound interest is calculated every day, week or year.

Every time the interest is calculated, the interest already earned is added to the investment amount. Most bank accounts compound interest daily, but it can be compounded on a weekly, monthly or annual basis.

The magic of compounding is that the interest grows at an increasing rate.

The following example will show you exactly what kind of effect compound interest can have on your money:

Would you rather have $10,000 every day for a month or a penny that doubles every day for a month?

Most people will laugh at the idea of taking the doubling penny, but it turns out that this option earns you more than 15 times what the $10,000 does. If you thought of the correct answer while reading, pat yourself on the back!

Still don’t believe in the magic of compounding?

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If you take the doubling penny, you will end up with $10,737,418 vs. $310,000 at the end of 31 days collecting $10,000 per day. Now, that’s the magic of compounding interest.

Simple vs. Compound Interest

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Simple Interest Example: Let’s say we deposit $1,000 in a bank account paying 5 percent interest a year. We plan to leave the money in the account for three years.

If the interest was calculated using the simple interest formula it would be:

Initial Amount x (rt)

r is the interest rate as a decimal, t is the number of time periods

So, the interest is:

$1,000 x (0.05 x 3) = $150

The total including the initial investment and the final amount is Initial Amount x (1+rt):

$1000 x (1+0.15) =$1,150


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Compound Interest Example: If the interest was compounded annually we would calculate the interest after each year, and add it to the initial amount at the start of the following year:

Compound interest can be calculated using the following formula:

Initial Amount x (1+r)t

r is the interest rate as a decimal, t is the number of time periods

So, the compound interest is:

Year 1: $1,000   x (1+0.05) = $1,050

Year 2: $1,050   x (1+0.05) = $1,102.5

Year 3: $1,102.5 x (1+0.05) = $1,157.63

After three years we would have $1,157.5, rather than the $1,150 we would have if we earned simple interest.

For our example it would look like this:

$1,000 x (1+0.05)3 = $1,000 x 1.157   = $1,157.63

However, if the interest is compounded monthly, we need to multiply the periods (t) by 12 and divide the interest rate (r) by 12:

$1,000 x (1+0.00417)36 = $1,000 x 1.1615 = $1,161.5

The final amount is higher because the interest was compounded more often.



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Fun Facts:


  • According to Warren Buffett, founder of Berkshire Hathaway, “My wealth has come from a combination of living in America, some lucky genes, and compound interest.”


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